University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2020
Views:

105

Pages:

2
Author:

Arielle Armstrong

Answer Key 6.1-6.2 REVIEW In Exercises 1-4, match the function with its graph. 1. y = 3^x 2. y = (1/3)^x 3. y = 2(1/5)^x 4. y = 5^x Exponential Growth or decay? State the growth or decay rate. Then graph the function. 4. y = 3^x Growth 400%↑ 5. y = (1/3)^x Decay 200%↓ 6. y = (1/2)^x Decay 50%↓ 7. y = (3/2)^x Growth 50%↑ 8. y = (1.6)^x Growth 60%↑ Use the graph of f(x) = b^x to identify the value of the base b. [Image of two graphs] y = 8^x y = 2^x 12. The value of a rare coin y (in dollars) can be approximated by the model y = 0.25(1.06)^x, where t is the number of years since the coin was minted. a. Exponential growth or exponential decay? b. Annual percent increase or decrease? c. What was the original value of the coin? $0.25 d. Estimate when the value of the coin will be $4.00? 15 years after minted 17. You invest $4000 in an account to save for college. Option 1: 5% annual interest compounded semi-annually. Balance in the account after 2 years? $4415.25 Option 2: 4.5% annual interest compounded continuously. Balance in the account after 2 years? $4376.70 Simplify the expression: 1. 4000(1+0.05/2)^(2*2) 2. 3e^3 3. 12e^5 / 36e^2 4. √(16e^(6x)) = (16e^(6x))^(1/2) 5. (3e^(3x))^2 6. √(16e^(10x)) = (16e^(10x))^(1/2) 7. Describe and correct the error in simplifying the expressions. X(2e^(2x))^2 = (2)^2(e^(3x))^2(x^2) = 4e^(6x)x^2 In Exercises 8-10, tell whether the function represents exponential growth or exponential decay. Then graph the function. 8. y = (1/4)^x Decay 9. y = 4^x Growth 10. y = (4/3)^-x Decay **Remember: logs = exponents + Base Stays the same** Rewrite in exponential form. 1. 2 = 8^3 2. 7^1 = 7 3. 5^2 = 25 Rewrite in logarithmic form. 4. log₄16 = 2 5. log₅1 = 0 6. log₆(1/6) = -1 Evaluate the logarithm. 7. log₄16 = 2 8. log₅125 = 3 9. log₆6 = 1 10. log₂(1/2) = -1 11. log₁1 = 0 12. log₃(1/3) = -1 Evaluate using a calculator. Round to three decimal places. 13. log 5 = 0.699 14. ln 14 = 2.639 15. log₁₀(1/4) = -0.602 **If they have the same base, they cancel out.** Simply: 17. 5^log₅x = x 18. e^lnx = x 19. 2^(log₂4x) = 4x Find the inverse of the function. 20. y = 1.1^x x = 1.1^y log₁.₁x = y 21. y = log₃x x = log₃y 3^x = 3^log₃y x = y 22. x = e^5y ln x = ln(e^5y) ln x = 5y y = (1/5)ln x 23. y = log(1/3)x x = log(1/3)y 10^x = (1/3)y y = 3*10^x 24. y = e^x/3 x = e^y/3 ln x = ln(e^y/3) ln x = (1/3)y y = 3ln x 26. The wind speed s (in miles per hour) near the center of a modeled tornado can be approximated by the model s = 93log d + 65, where d is the distance (in miles) that the tornado travels. a) A tornado traveled 35 miles. Estimate the wind speed near the center of the tornado. s = 93log35 + 65 ≈ 208.6 b) The wind speed near the center of a tornado was 150 miles per hour. Find the distance that the tornado traveled. 150 = 93logd + 65 d ≈ 17.3 **Graph:** a) y = log x b) y = ln x c) y = log₂x [Image of three graphs]