University:
Carleton College
Course:
MATH 120 | Calculus 2
Academic year:

2019
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98

Pages:

8
Author:

larbiwxcvbn

Advanced Math 4.2-4.3 Exponential Functions & Logs Name: 1. Name the two types of exponential functions and give an example of each type. Type 1: Growth Example: y = 4(1.05)^x Type 2: Decay Example: y = 4(0.95)^x Determine which of the following functions are exponential growth and which are exponential decay. Circle your answer. 2. y = 0.2^x GROWTH DECAY 3. y = 4^x GROWTH DECAY 4. A = 6(0.5)^t GROWTH DECAY 5. A = 1000(1.25)^x GROWTH DECAY Graph the given exponential function using the following domain for x: [-2, 2]. State whether the graph shows exponential growth or decay. 6. y = 3^x Growth 7. y = (1/3)^x Decay Rewrite each equation in its exponential form. 8. log₆10000 = 4 6⁴ = 10000 9. log₄0.25 = -1 4⁻¹ = 0.25 10. log₈512 = 3 8³ = 512 11. ln e² = 2 e² = e² 12. log₅(1/125) = -3 5⁻³ = 1/125 13. log₂(1/64) = -6 2⁻⁶ = 1/64 Rewrite each equation in its logarithmic form. 14. 4⁵ = 1024 log₄1024 = 5 15. 36⁰.⁵ = 6 log₃₆6 = 0.5 16. 7³ = 343 log₇343 = 3 17. 3⁶ = 729 log₃729 = 6 18. 100⁴ = 1024 log₁₀1024 = 4 19. 3⁻⁴ = 1/81 log₃(1/81) = -4 Solve each exponential or logarithmic equation. 20. log₂x = 2 2² = x x = 4 21. log₈512 = x 8^x = 512 8^x = 8³ x = 3 22. 4^x = 1/64 4^x = 4^-3 x = -3 23. log₂(1/32) = x 2^x = 1/32 2^x = 2^-5 x = -5 24. log₂64 = x 2^x = 64 2^x = 2⁶ x = 6 25. ln e⁴ = x e^x = e⁴ x = 4 26. 4^(2x-1) = 1/16 4^(2x-1) = 4^-2 2x - 1 = -2 2x = -1 x = -1/2 27. 5^(3x) = 25 5^(3x) = 5² 3x = 2 x = 2/3 28. 2^x = 128 2^x = 2⁷ x = 7 29. 7^(x-2) = 1/49 7^(x-2) = 7^-2 x - 2 = -2 x = 0 30. 7^x = 7^1/2 x = 1/2 31. 6^(4x+5) = 1/216 6^(4x+5) = 6^-3 4x + 5 = -3 4x = -8 x = -2 Evaluate without a calculator. 32. log₁₀1000 = x 10^x = 1000 10^x = 10³ x = 3 33. log₅1 = x 5^x = 1 x = 0 34. log₃(1/27) = x 3^x = 1/27 3^x = 3^-3 x = -3 35. log₄4³ = x 4^x = 4³ x = 3 36. ln e⁵ = x e^x = e⁵ x = 5 37. ln e = x e^x = e x = 1 For the following application problems, show the equation (if one hasn't already been given to you) and show the substitution of all the variables necessary to solve. Points will be given on the quiz for this work! 38. The attendance for a basketball team declined at a rate of 5% per game throughout the losing season. Find the attendance at the 15th (t = 14) home game if 23,000 people were at the first game. Round down to the nearest person. A = P(1 - r)^t A = 23000(1 - 0.05)^14 A ≈ 11216.5 ≈ 11216 39. The number of pay phones in use in the U.S. has been declining (due in large part) to an increased usage of cell phones. The function A = 2.28(0.9)^x can be used to model the number of pay phones (in millions) x years since 1999. a. According to this equation, how many pay phones were there in the U.S. in 1999? P = 2.28 million b. What is the rate of decline? 1 - r = 0.9 -r = -0.1 r = 10% c. How many pay phones were there in the U.S. in 2005? Round down to the nearest payphone. A = 2.28(0.9)^6 ≈ 1.21 million t = 6 40. Kristin starts an experiment with 7500 bacteria cells. After 4 hours, there are 23,000 cells. a. What is the rate of increase? A = P(1 + r)^t 23000 = 7500(1 + r)^4 2.067 = (1 + r)^4 1.3233 ≈ 1 + r r ≈ 32.33% b. How many bacteria cells can be expected in the sample after 12 hours? A = 7500(1.3233)^12 ≈ 216,252.4 41. An investment pays 4.2% interest compounded monthly. If $25,000 is invested in the account, what will be the balance after 15 years? Round to the nearest hundredth. A = P(1 + r/n)^(nt) A = 25000(1 + 0.042/12)^(12*15) A ≈ $46,888.66

Math 4.2 Logs and Exp. Functions Solution Key

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