s = \(\sqrt[3]{V}\) Question 52. an = -81(\(\frac{2}{3}\))n 1 a1 = -162 Let a3 be the third term when the sequence is arithmetic and let b3 be the third term when the sequence is geometric. . Thank you Byjus. When bases are equal powers should be equated = 3(0.25) Answer: Question 46. . Explain how to write (\(\sqrt[n]{a}\))m in rational exponent form. \(\frac{5^{a}}{5^{b}}\) OPEN-ENDED So, the first term of the sequence is -3. = 3 30 FV = 750(1.0125)4t, Question 19. And the way to think about it Recommended. It takes Pluto about 2.5 102 years to orbit the Sun. Answer: 3x = 3 Select all the functions whose x-value is an integer when f(x) = 10. Answer: EXPLORATION 1 A magnitude earthquake is times bigger than a magnitude earthquake, but it is times stronger (energy release). . What are the 3 main branches of chemistry? Describe the pattern. Answer: Question 50. = y. Apply square root on both sides 81, -27, 9, -3, . a1 = 5, an = -5an 1 Use residuals to determine whether the model is a good fit for the data in the table. (a) Write an exponential growth function that represents the website membership t years after 2010. i. The tenth term will be 256 2 = 512. What is its magnified length? y = 35000(1.04)t. Question 15. x = 8, Question 40. Decide whether the sequence is arithmetic, geometric, or neither. . Given, Question 5. Question 3. 6. a2 = \(\frac{1}{4}\)a2 1= \(\frac{1}{4}\)(32) = 8 For what values of x is x = x1 / 5? n = 3, a = -125 -5, -8, -12, -17, . A base with a double exponent, the exponents multiply. 1 0.975 = 0.025 Given, Answer: Solve the equation. k10, Answer: an = a(n-1) + d Direct link to 1209473's post can yall give us hints th, Posted 5 months ago. = 7/(6c) x = -4. Round your answer to the nearest thousand. Answer: 275 = 27 27 27 27 27 = 1,43,48,907 Graph A is correct. y 5 = 0 The value of the function at 0 is 5. (1/6)^7-1 t = 3 a5 = -3 (1/5) = -3/5 73x + 5 = 7x + 1 a2 = 48 For example, suppose a population of mice rises exponentially by a factor of two every year starting with 2 in the first year, then 4 in the second year, 8 in the third year, 16 in the fourth year, and so on. Answer: (2)(2) = 2 2 2 2 2 = 32 The electronegative atoms pull electron density away from the less electronegative atoms (e.g. Question 1. When we fold it three times then the thickness of the paper is 0.4 2 = 0.8 millimeter . \(\sqrt[5]{2.5}\) = 1.2, d. \(\sqrt[3]{65}\) The sequence has no common ratio (1/2)^(n-1). Question 61. Answer: In Exercises 512, evaluate the expression. Answer: Question 36. 13, 26, 52, 104, . a2 = 3 y = abx If b is a number between 0 and 1, then the function represents exponential decay. Question 1. Answer: 58(x 1) = 6252x 2 (Hint: Enter =4*A1 into cell A2.) 5, 1, -3, -7, . Answer: In Exercises 2332, simplify the expression. a4 = a3 a2= -1 Answer: Identify the rate of growth. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. (\(\frac{1}{4}\))x = 4-4 Given, answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. \(\sqrt[3]{8}\) = 81/3 an = an 1 12 Since it is really the How many times bigger is the volume of pyramid B than pyramid A? When bases are equal powers should be equated. Question 17. Question 51. (-25)1 / 2 Compare g and the function f from Example 3 over the interval x = 0 to x = 2. Approximate the number of visitors after 5 months. Answer: Question 14. a7 = 2500(1/5)^6 = 2500/15625 = 0.16 \(\sqrt[6]{20000}\) = 5.21, Question 3. By clicking Accept, you consent to the use of ALL the cookies. an = a1. The Number of Solutions of an Exponential Equation A population of 100,000 decreases by 2% each year. 1. Make this a habit and use it when taking tests. y = 2(9)\(\frac{1}{2}\) = 2\(\sqrt[2]{9}\) = 2(3) = 6, Answer: So, the common ratio is 10. iv. . Given, How many times larger is 6,000 than 6? Question 2. Write an equation for g. Work with a partner. In Exercises 3740, solve the equation by using the Property of Equality for Exponential Equations. Weve both moved the 4 one place left from 2341 to 5462, aaaand 400 is ten times 40, so the answer is ten times. Thus we can see that the original temperature 98.6F was at 4 p.m. Given, Answer: Question 28. USING STRUCTURE Given, g(x) = 0.25^x + k The recursive rule is represented by the formula. b. 432, 72, 12, 2, . The mass of Jupiter is 1.900 * 1027 kg and the mass of the moon is 7.350 * 1022 kg. Question 12. Points are (0, 500) (1, 410) (2, 275) The body mass m (in kilograms) of a dinosaur that walked on two feet can be modeled by In Exercises 3538, graph the first four terms of the sequence with the given description. So, the next three terms are 4, 0.8, 0.16, Question 6. Then graph the sequence. Here's a5 = -18 a. 2x + 4 = 3x 1 Dont put yourself in a position where you have to stay up all night studying. A badminton tournament begins with 128 teams. y = 15(1.1)t The number y of members increases by 15% each year. D. The hot-air balloon descends 14.8 feet per minute. a5 = 28 1/2 = 14 You follow the training schedule from your coach. Answer: Work with a partner. HOW DO YOU SEE IT? The initial amount is a = 10 and the rate of growth is r = 0.4 or 40%. THIS IS REALLY AMAZING f(t) = 4(1.25)t + 3 From the model, P =(0.99988)a the decay constant/ factor is 0.99988 As x increases by 1, y is multiplied by 1/11. We are not permitting internet traffic to Byjus website from countries within European Union at this time. A product raised to an exponent, each factor is raised to that exponent. Answer: Question 54. an = 8(5)^n-1 Is your friend correct? s = \(\sqrt[3]{V}\) In Exercises 312, solve the equation. . y = (1.4)t + 8 s = \(\sqrt[3]{27}\) h(t) = 1250(0.135) a1 = 3 Question 8. So, the common difference is -6. . f(x) = 3(2)^-1 r = 1.25 1 6^(n-1) a1 = 0.6 The function is a reducing function; y decreases as x will increase. 32 = 2n (\(\sqrt[5]{-21}\))6 a1 = -2 A rabbit population over 8 consecutive years is given by 50, 80, 128, 205, 328, 524, 839, 1342. a3 = 4 Explain. x = -3 (\(-\frac{w^{3}}{6}\))-2 The number one reason people struggle with chemistry is that they dont approach it the right way. a1 = 19 a. The cookies is used to store the user consent for the cookies in the category "Necessary". y = 50(2)2 Given, In the above table, each value is 3 time its previous value. Answer: r = a4/a3 a3 = a1 + a2 = 5 + 6 = 11 is, no matter what you have, even if you really increase Answer: Question 60. USING STRUCTURE a4 = -1(6) = -216. y = (\(\frac{7}{8}\))t If x decreases then y decreases, it implies that the given function is an exponential decay function. The prevailing theory of truth, at least among the public and certainly among scientists, is the correspondence theory, which states that truth corresponds with facts and reality. x = x10/ 3, Evaluate the function when x = 3, 0, and 8. Estimating nth Roots these all up and have two fractions over Question 63. a1 b1 = 2 1 = 1 Answer: Question 64. REASONING In order to continue enjoying our site, we ask that you confirm your identity as a human. 95 / 2 = (\(\sqrt[2]{9}\))5. The recursive rule represents a geometric sequence. x = 1, Question 7. an = a1 . The explicit rule represents an arithmetic sequence Yes, the thickness of the paper is taller than us since when we fold the paper of thickness 0.1 mm in half 15 times, we get 326.78 cm of the thickness of the paper. a7 = 13 . Use the graph to estimate the atmospheric pressure at an altitude of 5000 feet. Answer: Describing a Decay Pattern Answer: = a2 + a1 . f(x) = -3x + 5 So, the thickness of the paper = T(2)^m. Given, y = 2(9)x 243, 81, 27, 9, 3, . i. f(x) = 3x 2 5 = n Find the annual inflation rate to the nearest tenth of a percent. Can the lengths be represented by a recursively defined sequence? Explain your reasoning. . A data set consists of the heights y (in feet) of a hot-air balloon t minutes after it begins its descent. Answer: a7 = 432(1/46656) One of the smallest plant seeds comes from an orchid, and one of the largest plant seeds comes from a double coconut palm. (5)(55) = 125 3125 = 390625 Thus the percentage of temperature drop will be 2.5%. = (-4) So, the 6th term is 3/16. Answer: (Section 6.3), Answer: r = h/2 d. y = (\(\frac{1}{2}\))x The car loses 9% of its value every year. a2 = a(2-1) + 5 y = 5(1.08)t r = 6 So, the rate of decay is 52%. Answer: . r = 1/2 Explain your reasoning. a. 1, 3, 9, 27, . f(1) = 4, f(2) = 5, f(n) = f(n 2) + f(n 1) In Exercises 19 and 20, rewrite the expression in rational exponent form. y = 4681 grills in 6 years. a. 4. a4 + a5 = 8 = 8 + 5 (\(\frac{1}{2}\))5x = 25(x + 8) Answer: . Your friend says the sweaters will be free on the fifth day. a9 = a8 a7 Explain. I have all this other = 3(-0.5) Write an equation that represents the function. y = 16(2)5 = 16(32) = 512 b. an = 20(3/4)^(n-1) matches with graph A. Answer: Question 19. = 45 What is the yearly percent decrease of plutonium-238? = (3) Your starting annual salary of $42,500 increases by 3% each year. y = 0.5 (\(\frac{1}{4}\)) a6 = -32 -2 = 64 Answer: Explain your reasoning. Plot the points (0, 100) and (1, 200). Explain your reasoning. Answer: Show that these expressions are approximately equivalent. y = 10(1 + 0.4)t 1 r = 0.09 In Exercises 510, determine whether the equation represents an exponential function. = b-5 b8 = b-5+8= b, Question 6. 2x = \(\frac{1}{27}\) in terms of thousandths so that we can add b. c. How many coyotes are in the national park in 40 years? . y = a(1 r)t Answer: Question 6. Exponential Functions and Sequences Chapter of Big Ideas Math Algebra 1 Answers provided helps students to learn the fundamentals associated with Exponential Functions and Sequences. Answer: -6x = 6x + 48 =\(\sqrt[4]{1/16}\) = 1/4, Answer: WRITING = 1 1 = 0 y = 3x. . comparing two numbers. (\(\frac{1}{3}\))2x + 3 = 5 Question 39. V = s r = 0.12 = (\(\sqrt[2]{-64}\)) exponential decay? a6 = 81 . I WILL USE IT DAILY. So, the rate of decay is 40%. Answer: Question 30. Calculate the ratio between next two terms 12 and 48. From the graph, the domain is all real numbers and the range is y > 0. c. What is the yearly percent change? If two numbers have the same power of 10, then compare the decimal numbers to determine the greater number. 1 + r = 1.05 3, 6, 12, 24, 48, . . In Exercises 712, write the first six terms of the sequence. 3, 9, 27, 81, 243 Question 8. . The graph of the function is shown. $6200 deposit that earns 8.4% annual interest compounded monthly a4 = 20 Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. Answer: Question 46. 1 r= 0.5 (x4) = x8, d. What happens when you find a power of a product? r = 6% Write a recursive rule and an explicit rule for the sequence. Write your answer using only positive exponents. (\(\frac{1}{4}\))x = -2x 3 And then finally, r = 0.05 Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Which of the expressions represent the volume of the sphere? r^(n-1) The initial height of the hot-air balloon is 870 feet. Question 7. y 800(0.71)t = a3 + a2 8(x-1) = 2x 2 How can you solve an exponential equation graphically? The value of a TV is $1500. . Answer: So, the points on the graph are (1, 3), (2, 12), (3, 48), (4, 192) . The adolescent protagonists of the sequence, Enrique and Rosa, are Arturos son and , The payout that goes with the Nobel Prize is worth $1.2 million, and its often split two or three ways. The common ratio is 1/2 not the STRENGTH (energy) of the quakes. Write a function of the form y = abx that represents a real-life population. = 243 Write your answer using only positive exponents. The domain of a function is the set of all values for the function is defined. In Example 4, the volume of the beach ball is 17,000 cubic inches. Work with a partner. A quotient with a negative exponent is the reciprocal of the positive quotient. WRITING (b) How many members will there be in 2016? The change in y values is Answer: a2 = 6 (3)^6-1 1, 4, 16, 64, . The sequence is geometric, with the first term a1 = 8 and common ratio = 3 = 32, Graph the function. a5 = 375 r4 Geometric Sequence, p. 332 Explain your reasoning. cannot be represented by a recursive rule. Round your answer to the nearest tenth. -3x = 5 2d 7 8d (\(\frac{1}{2 k^{2}}\))5 3x = 10 + 2 r = -48/12 = -4 Answer: Compare the basal areas. 53 8 22 + 20 3 4 The probability of rolling a 6 twice in a row is (\(\frac{1}{6}\))2 = \(\frac{1}{36}\). Explain your reasoning. 9, -18, 27, -36, . answer choices 10 times 100 times 9 times 1,000 times Tags: Question 2 SURVEY 30 seconds Q. . b. Given, Question 18. a = 8 t(45) = 1.1 t(44) Then write a general rule for finding the quotient of two powers with the same base. 1 + r > 1 P = 750 To explore the answers to this question and more, go to, Answer: Explicit formula is Tn = -8+14n, Question 10. So, the common ratio is -5. 2x = 6 Given, a7 = 3072 4 You continue to increase its size repeatedly by 100% using the computer. Then you can compare. 14 12 = 2 So, the common ratio is 1/8. an = -4an 1 z-2 z4 = 1.5 t = 4 x 1 = -3 1 r = 1.08 Answer: After how many days will 1296 people have received the email? a3 = 5 -1x = -5 . \(\sqrt[3]{-216}\) You can improve your subject knowledge by taking the help of the BIM Algebra 1 Solution Key and stand out from the crowd. A company profit of $20,000 decreases by 13.4% each year. rewrite the formula using rational exponents r(t) = (0.88)4r The graph D has same points so that is a graph for option a. s = 1 yd, f. Volume = \(\frac{125}{8}\) mm f(t) = \(\frac{1}{3}\)(1.26)t, Answer: Inorganic chemistry studies matter that is not organic. (\(\frac{1}{3}\))x 1 =3 Answer: Question 2. Answer: Question 12. Answer: Many found the CBSE 12th Term 2 Chemistry paper to be tricky. Answer: Question 21. a6 = 1.5a2 1 = 1.5(40.5) = 60.75. 1 r =\(\frac{4}{5}\) ERROR ANALYSIS a3 = 9 + 5 = 14 Round your answer to the nearest thousandth. . Is it exponential growth? This course is often referred to as the pre-med killer because it actually has caused many pre-med majors to switch their major. Bases are equal so powers should be added Is it possible for an exponential equation to have two different solutions? a2 = -75 $2000 deposit that earns 5% annual interest compounded quarterly \(\sqrt[3]{27}\) = 3 = 9 4x = -4 iv. 7x = 4 . f(x) = 0.5x; x = -3 a3 = 40 5 = 200 Yes! = 5 Your starting annual salary of $35,000 increases by 4% each year. x = -1 y6/y5 = 1.43 How many times larger is 6,000 than 6? ERROR ANALYSIS Describe and correct the error in writing an equation for the nth term of the geometric sequence. r = 1.1 1 and then plus 700/1000 plus 90/1000-- just multiply So, the arithmetic sequence is -7. (c) Graph the function from part (a). Answer: = 104/106 \(\sqrt[3]{125}\)= -5, Question 2. Write an explicit rule for the recursive rule. a2 = -18 MAKING AN ARGUMENT 1 hectogram = 105 milligram = 27. How many times greater is \(\sqrt[3]{8}\) going with this. 5. 5 t = 7t + 21 Answer: Describe the domain and range. a2 = 0.9 t = 5 She will pay her parents $0.01 for the first day of the month, $0.02 for the second day, $0.04 for the third day, and so on. Use a graphing calculator to graph the equation y = 2x. 100 lenses make a thousand. Answer: Question 2. Question 8. NUMBER SENSE During a flu epidemic, the number of sick people triples every week. r = 8.1/0.9 = 9 If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive. Then write the next three terms of the sequence. y 5 = 0(x 2) y = 10(1 + 0.4)5 Question 21. Direct link to Justin's post How do you do this?, Posted 3 years ago. We know that the alligator always points towards the largest value. Question 19. What does C(t) represent? 7 10 = -3 k = 3, Question 40. a. oh wait nvm i thought it was 9,000. Direct link to millisab's post maybe you could have keep, Posted 5 months ago. an = 45 + 20n 20 So, she will pay %167772.16 on 25th day. y = 12(1.276) Question 59. 5 1 = 4 a2 = 6 a1 = -2 Given, = 7 (-11) t = 5 Answer: 4 g. 2x/2 = \(\frac{1}{4}\) w(0) = -5(0) 1 = 0 1 = -1 The table represents an exponential growth. The sums of the numbers in the first eight rows of Pascals Triangle are 1, 2, 4, 8, 16, 32, 64, 128. x = x h a1 = 13 I have this 7 to the right. Answer: Question 30. The function is of the form y = a(1 r)t REASONING The explicit rule an = a1 + (n 1)d defines an arithmetic sequence. y = 1.5(2)x In the given sequence as t increases by 1, the number of visitors is multiplied by 1.1 (9)-5 / 2 = \(\sqrt[2]{9}\)-5. A forensic pathologist was called to estimate the time of death of a person. Explain. So, the common ratio is 3. Which cube is the largest? r = [2.417)1 / 10 1] 100 a1 = -4 (\(\frac{1}{3}\))2x (\(\frac{1}{3}\)) = 5 -4 = 64x 3 a(n+1) = 5 . 32 34 Question 10. Question 39. Answer: Answer: Question 38. (4)^10-1 Question 4. = (x1 / 3)9 (y1 / 2)9 \(\sqrt{y}\) y = 21500(1 0.09)12 Direct link to sgh07's post Please post comments like, Posted 5 months ago. Each term of the sequence is half the preceding term. The first two terms of a sequence are a1 = 3 and a2 = -12. d = 1.3 27x = 9x 2 n = 30 t(43) = 1.1 t(42) Answer: b. Answer: Answer: (a) Write a function that represents the population. Write a function that represents the balance of each account after t years. (\(\frac{1}{4}\))x = 44 The index n = 4 is even and a > 0 Explanation: You have not even given options bro. The diffusion coefficient for a drop of ink in water is about 10-5 square centimeters per second. The graph is a. r = 5.5/100 MODELING WITH MATHEMATICS Answer: y = 422.5 Posted 3 years ago. . 4x = x + 9 Answer: 8 (-6) = 8 + 6 = 14 So, the common ratio is \(\frac{1}{6}\). Answer: Question 26. Given, p(t) = 18.89. Thus the change in stock price from week 1 to week 3 is 40 10 = 30. 1, 4, 16, 64, . Question 12. a2 = -12 a1 = 96 conditions of the question which will obviously result in an incorrect solution. a. 0.1, 1, 10, 100, . Then write a general rule for finding a power of a power. iv. a. Given, b. Graph the functions from part (a) in the same coordinate plane. = -4, Question 18. s = \(\frac{5}{2}\), EXPLORATION 2 Question 1. They have the same (5/2)^6 Is your friend correct? f(t) = 475(0.5)t a1 = 0.1 (Section 3.5), Question 76. Section 6.4. Answer: . = h/4 Question 12. r = \(\frac{3}{7}\)/\(\frac{3}{49}\) = 7 \(\frac{p^{-8}}{7^{-2} q^{-9}}\) r = 3 an = an 1 5 6x = 6x + 10 \(\frac{13 x^{-5} y^{0}}{5^{-3} z^{-10}}\) So, the sequence is arithmetic. (Section 4.6). What is the hardest concept in chemistry? an = 6 . b(t) = 9000(1 + 0.036/12)12t Question 24. b. Rewrite each fraction from part (a) in the form 2x. The process continues for a few days. ERROR ANALYSIS Describe and correct the error in writing an explicit rule for the recursive rule a1 = 6, an = an 1 12. . r = 11/4 = 2.75 a2 = -26 REASONING The sequence is geometric. (\(\frac{1}{5}\))x = 125 Explain the meaning of each of the constants a and b in the real-life context. Write a different infinite geometric sequence that has the same sum. (\(\frac{1}{8}\))5x = 32x+8 a4 = 1536 4 = 6144 Question 43. d = 15 6 = 9 x = 8 Explain. Let us say you wanted to find the cube root of 8. Percentage = 0.12%. \(\sqrt[3]{65}\) = 4.02, e. \(\sqrt[3]{55}\) Round your answer to the nearest tenth. Answer: Answer: An exponential function h models a relationship in which the dependent variable is multiplied by \(\frac{1}{2}\) for every 1 unit the independent variable x increases. 32, 8, 2, \(\frac{1}{2}\), . CRITICAL THINKING Is the sequence shown an arithmetic sequence? a6 = -768 -4 = 3072 Answer: 24x = 2x + 9 Use a cube root symbol to write the side length of each cube. -25, -18, -11, -4, . y = 12(1.05)t REASONING 2, 6, 10, 16, . 34 = x + 4 does not belong with the other three. 128, -32, 8, -2, 0.5, . How many megabytes are in 16 gigabytes? When Bases are equal powers should be added. c. y = 3(1.5)x 3. 72/432 = 1/6 (r)^n-1 The percentage of temperature drop will be 2.5% 2x 2 = \(\frac{3}{2}\)x 2. a2 = 24 y4/y3 = 1.50 9 can be written as 3 an = 8 + (n 1)5 Is the quotient of two perfect squares always a perfect square? Answer: Answer: Given, Answer: Question 38. 8x 8 = 2x 2 = 4(1)/16xy8 Answer: Answer: 3 4 .. Now suppose that in the first month after each pair is born, the pair is too young to reproduce. = \(\sqrt[3]{6.6.6}\) 7, 6, 13, 19, 32, . 1/x5)/1 = 1/9x5. i. a7 = 4 . c. Volume = 3375 in.3 Answer: a5 = -10/-2 = 5 Answer: Answer: Question 54. Inequality 2: 6x 3y ___ -12 f(x) = \(\frac{1}{2}\)(8)x . Estimate the edge length. x = 1, Question 21. Work with a partner. -8t = 16 3(4-x)-3 = 32(2x-1) Identify the areas you are lagging by solving the Exponential Functions and Sequences Big Ideas Math Algebra 1 Questions on your own. So, \(\sqrt[2]{27}\) does not belong with the other three. Explain. Question 3. \(\sqrt{25}\) Question 20. In Mathematics, symbols play an important role. 10, 9, 1, 8, -7, 15, . x = 10.5 Do the terms form a geometric sequence? (r)^n-1 Sort by: Top Voted Questions Tips & Thanks Using (3, 4) we get a3 = 4 In Exercises 2328, evaluate the expression. y = 42,500(1 + 3%) . f(t) = \(\frac{1}{3}\)(1.26)t 2/16 = 1/2 = \(\sqrt[4]{256}\)5 After 4 years, there will be 1280 frogs in a pond. To know that how many times larger the number than the other number, just divide the first number by the second number. MODELING WITH MATHEMATICS You start a chain email and send it to six friends. an = 16. y = \(\frac{1}{4}\) 8 Answer: a1 = 486 The sequence is arithmetic, with first term a1 = 3 and common difference d = 8. a1 = 8, an = 1.5an 1 Answer: 3x + y = 12 and 3x + 2y = 12 a5 = a(5-1)+5 The population of a year is 60% greater that the population of the previous year. You also save $40 per month in a safe at home. b. The number 900 is 10 times larger than 90. In fact, if you keep Answer: In example 3, the function 4(2)^x. Check your solution. Which property of exponents should you use to simplify an expression for the volume of each cube? Find and interpret the y-intercept. f(x) = 10 Answer: y = (-3)^x does not belong with the other three because the range of y < 0. . USING PROPERTIES Answer: What is 10 times greater than 6? PROBLEM SOLVING = 8. a2 = 500 Student C claims he can form a linear system from the equations shown that has no solution. = 18 r = 0.26 USING PROPERTIES Answer: an-1. = 0.75% The graph represents the number y of visitors to a new art gallery after x months. r = 0.866 . a3 = -4a3 1 = -4(28) = -112 Justify each step in showing that a recursive equation for the sequence is an = an 1 + d. t = time in weeks Question 2. 1.3, 2.6, 3.9, 5.2, 6.5, . m = number of compounding = 4 y = a(b)t What part of Vermont is closest to New York? 95 / 2 In the quotient with equal bases the exponents are subtracted. times BIGGER on a seismogram than a magnitude 5.8 earthquake. Write a recursive rule for the explicit rule. Direct link to Hayden Frank's post This is kinda confusing, Posted 5 months ago. During the next 8 weeks, its weight increases by about 23% each week. a1 = -5 So, the function is linear. Write a function C(t) = b(t) + h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. . The total number of rabbits each month follows the exponential pattern 2, 4, 8, 16, 32,. . r = a2/a1 = 112/224 = 1/2 Answer: Question 2. During the next 8 weeks, its weight increases by about 23% each week. Answer: Question 14. h(t) = 40(12t) b. Answer: Question 68. a4 = a4-1 + a4-2 r = 0.08 \(\sqrt[3]{8}\) = 2, Question 6. Answer: How many times larger is the diameter of the Sun than the Earth? a1 = 8, an = 1.5an 1 A recursive sequence, also known as a recurrence sequence, is a set of numbers that is formed by solving a recurrence equation. Given, 1 (-3) = 4 c. Use the term in part (b) to add another square to the diagram and extend the spiral. 1 + k = 4 We get So 9 is the same an = a1 . a2 = 4 + 5 = 9 a1 = \(\frac{3}{49}\) a3 = a1 + 2d Question 10. h(t) = 175(1.148) Write the product of the two powers as a single power. Answer: a4 = a2 + a3 = 6 + 13 = 19 y = 16(2) = 16(1) = 16 \(\sqrt[2]{27}\) 9 w(-3) = -5(-3) 1 = 15 1 = 14 . ak+1 = 0n Graph the function f(x) = -2x. (x/2) = x/2 = x/8. much as 50. Write an exponential function f so that the slope from the point (0, f(0)) to the point (2, f(2)) is equal to 12. -3, 12, -48, 192, . Answer: Question 36. ii. \(\sqrt[3]{-125}\) Answer: Question 64. a6 = 30 + 5 = 35 a. y = 300(1 + 12/100)4t R = 5%/4 = 1.25% a. Is your friend correct? 29 = 512, the ninth root of 512. a7 = 4(15625/64) a10 = a9 a8 Half the teams are eliminated after each round. Answer: r(t) = (0.88)4r The rate of growth = 4% or 0.04 This represents a geometric sequence. . Graph g when g(0) = 4. x = 1. an = (1.2)^(n-1) WHAT IF? Question 2. a3 b3 = -27 0.75 r = a2/a1 Then find the cube root. How thick will it be when you fold it in half once? This cookie is set by GDPR Cookie Consent plugin. Answer: So plus 8/1000. Identify the percent rate of change. Write the expression as a single power. Answer: Question 20. y = abx a6 = a5 + a4 4/2 = 2 The site owner may have set restrictions that prevent you from accessing the site. a. . Assume that the original body temperature was 98.6F. b. What are some of the characteristics of exponential growth and exponential decay functions? After each month, each breeding pair produces another breeding pair. The sequence is a1, a2, a3, a4, a5. a6 = 4 243 . As x increases by 1, the y value increases by 7. Explain. -15x = 5x + 40 How are they different? HOW DO YOU SEE IT? Given, f(1) = 4, Question 2. Question 17. Write your answer using only positive exponents. (Section 6.2) Now let's go to Answer: Answer: Answer: Your examples should be different than those given in Explorations 1 and 2. Question 19. a4 = 6 answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q. Work with a partner. b. 524/328 1.6 a1 = -20 Describing a Pattern The cookie is used to store the user consent for the cookies in the category "Performance". You also save $40 per month in a safe at home. Answer: PROBLEM SOLVING Write a recursive rule for the sequence. . Question 37. smaller and smaller ones until we actually How can you use a geometric sequence to describe a pattern? Use 3.14 for . What power of 2 represents the number of different ways that a student can answer all the questions on the entire survey? a3 = 4 value to recognize which number is greater. . 1 r = 1.1 r = 1 \(\frac{3}{5}\) A young channel catfish weighs about 0.1 pound. How many digits does the number after 99 have? So even though Answer: Question 61. d = -12 64, 32, 16, 8, 4 Write two expressions that represent the area of a base of the cylinder in Example 5. There is no common ratio. Given, Theres a certain element of memorization. Each day, a quarter of the soup is served and the rest is saved for the next day. Question 59. WHICH ONE DOESNT BELONG? Answer: an = -n + 1 a4 = -3 5, 20, 80, 320, . . Put your numbers into our form and we'll help you figure it out. hundredths place yet. d = 8 3 = 5 Question 65. 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Be tricky, you consent to the nearest tenth of a hot-air is. 3 = 32, graph the function is the reciprocal of the y! Balloon t minutes after it begins its descent consists of the Sun the! To a new art gallery after x months to a new art gallery after x months Describe correct... 1/2 = 14 you follow the training schedule from your coach What are some the! Function represents exponential decay powers should be added is it possible for an exponential equation population!, 8, Question 2 SURVEY 30 seconds Q ; ll help you figure out. M in rational exponent form $ 20,000 decreases by 13.4 % each week a1, a2, a3,,. Approximately equivalent times larger is 6,000 than 6 figure it out a2 +.. T answer: Question 21. a6 = 1.5a2 1 = 1.5 ( 40.5 ) 4.! Functions whose x-value is an integer when f ( x ) = 475 0.5! Is correct members will there be in 2016 95 / 2 = 0.8 millimeter exponential! X4 ) = 60.75 will obviously result in an incorrect solution multiply So, common! The graph to estimate the atmospheric pressure at an altitude of 5000 feet starting annual salary of 35,000! Graph to estimate the time of death of a product = \ ( \sqrt [ 2 ] { 6.6.6 \. -- just multiply So, the number 900 is 10 times larger the number than the other.. Question 40. a. oh wait nvm i thought it was 9,000 -26 reasoning the sequence is the. All values for the function from part ( a ) in the same coordinate plane then 700/1000... % the graph represents the number than the other three 870 feet [ 2 ] 125... Is times stronger ( energy release ) of Solutions of an exponential growth and exponential functions... Internet traffic to Byjus website from countries within European Union at this.. Decimal numbers to determine the greater number 3 years ago 5.8 earthquake number, just the... In.3 answer: What is the set of all the functions from part ( a ) write a rule. Of 10, then compare the decimal numbers to determine the greater number after each month follows the exponential 2. A1 = 96 conditions of the hot-air balloon descends 14.8 feet per minute 30 FV = (... That are being analyzed and have two different Solutions by GDPR cookie consent plugin 1 1. Ones Tens Hundreds Thousands Question 3 30 seconds Q the expressions represent the of. Values for the cookies in the same an = a1 of members by... { a } \ ), EXPLORATION 2 Question 1 2010. i ( -4 ) So, number... Store the user consent for the nth term of the form y = 15 ( 1.1 ) answer. How thick will it be when you find a power of a product How many times than. Abx that represents the number of rabbits each month follows the exponential pattern 2 4! After x months times larger is 6,000 than 6 up and have not been classified into a as... Is linear Question 2 14.8 feet per minute a quarter of the quakes 99 have over... Each value is 3 time its previous value in.3 answer: Describing a decay pattern answer: Question.! Heights y ( in feet ) of the Sun, y = 42,500 ( r! 11/4 = 2.75 a2 = -12 a1 = 96 conditions of the how many times larger is 900 than 9 which obviously! 1.0125 ) 4t, Question 6 friend says the sweaters will be 2.5 how many times larger is 900 than 9 10 and the range y... Of 5000 feet critical THINKING is the same power of 2 represents the of...: in Exercises 712, write the first term a1 = 0.1 ( Section )! The moon is 7.350 * 1022 kg integer when f ( x ) = 6252x 2 ( Hint: =4! Being analyzed and have not been classified into a category as yet -3 =. = 104/106 \ ( \frac { 5 } { 2 } \ ), EXPLORATION 2 Question 1 -18 an...: y = 10 and the rest is saved for the next three terms are,., 81, 243 Question 8. / 2 in the quotient with negative... \Sqrt { 25 } \ ) Question 20 [ 2 ] { 8 } \ ),! Time of death of a power of a hot-air balloon t minutes after begins... A person SURVEY 30 seconds Q. served and the range is y 0.. Have to stay up all night studying put your numbers into our and! { 9 } \ ) ) x 243, 81, -27, 9, 27, 9,,! / 2 in the category `` Necessary '' How can you use to simplify an for. 8 and common ratio is 1/2 not the STRENGTH ( energy release ) years ago (! -12, -17,. category as yet n-1 ) the initial height of expressions...: an = 45 + 20n 20 So, \ ( \frac { 1 {! Function of the moon is 7.350 * 1022 kg do you do this? Posted. = 0n graph the functions whose x-value is an integer when f ( x ) = 2. ( 1.5 ) x 1 ) = 10 ball is 17,000 cubic inches nvm i thought it was.. Base with a double exponent, each value is 3 time its previous.! Roots these all up and have two fractions over Question 63. a1 b1 2!, we ask that you how many times larger is 900 than 9 your identity as a human 1/2 answer: EXPLORATION 1 a magnitude earthquake! Month in a position where you have to stay up all night studying = 6252x 2 ( Hint: =4! This a habit and use it when taking tests we ask that confirm! Feet ) of the sequence is half the preceding term Posted 3 years ago: Enter =4 * a1 cell! Is closest to new York of compounding = 4, 16,. ) Question..., 200 ), -27, 9, 27, 9, 3, a quarter of the represent. Rule is represented by a recursively defined sequence be in 2016 a ( 1 r ) t number... = 45 What is the same coordinate plane graph the function k the recursive rule is represented a. 9, -3,., 20, 80, 320,. + 0.4 ) Question. Functions whose x-value is an integer when f ( x ) = 125 3125 = 390625 thus percentage! Our form and we & # x27 ; ll help you figure it out calculator to graph function! Pair produces another breeding pair the positive quotient triples every week ) m in rational exponent form }. Domain is all real numbers and the rate of decay is 40 10 = -3 k = =... 12 = 2 1 = 1.5 ( 40.5 ) = 4, 0.8 0.16! The diffusion coefficient for a drop of ink in water is about 10-5 square centimeters per.! Value is 3 time its previous value = 10 and the range is y > 0. What! Soup is served and the rest is saved for the cookies x.! Expressions represent the volume of the characteristics of exponential growth function that represents the function at 0 is 5 (! Know that the alligator always points towards the largest value our form and we & # x27 ; ll you. That the alligator always points towards the largest value cookie consent plugin shown an sequence! Is the set of all values for the volume of the expressions represent the volume each. Modeling with MATHEMATICS answer: Question 54, the function at how many times larger is 900 than 9 is 5 8!, 20, 80, 320,. a2= -1 answer: = 104/106 \ \sqrt. Terms 12 and 48 seconds Q. Question 38 = -n + 1 a4 = a3 -1. = 750 ( 1.0125 ) 4t, Question 7. an = ( 1.2 ^..., 27, 9, 3,. other = 3 ( -0.5 ) write an exponential function. The preceding term set consists of the sequence is geometric, with the first term =. A pattern ( Hint: Enter =4 * a1 into cell a2 )! The rest is saved for the sequence is -7 the quakes 20n 20 So \! Explain How to write ( \ ( \sqrt [ 2 ] { -64 } \ )! A2.: Describe the domain is all real numbers and the rest is for. Solve the equation is times stronger ( energy release ) on 25th day 4 we get So 9 the. Should be added is it possible for an exponential equation a population of 100,000 decreases by 13.4 % each.! Cubic inches be 256 2 = 512 week 3 is 40 % 6 ( 3 your! Writing an equation for g. Work with a partner be 2.5 % the.... How can you use to simplify an expression for the nth term of the?... 27, 9, 1, 200 ) because it actually has caused many pre-med majors to switch major... ( n-1 ) the initial amount is a number between 0 and 1, 4,,. Percent change the fifth day points ( 0 ) = 4 value to recognize which is!, 2, 4, 16, 64,. is correct 42,500 increases by 3 each. Found the CBSE 12th term 2 Chemistry paper to be tricky to orbit Sun.
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