Assignment

Answer all 22 exercises, and show all work in this word document.

1. Decide whether each function as graphed or defined is one-to-one.

a.

b. y = - √(100 - x²)

c. y = 4 / (x - 8)

2. Use the definition of inverses to determine whether f and g are inverses.

f(x) = 3x + 9,    g(x) = (1/3)x - 3

3. For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form y = f^-1(x) (b) graph f and f^-1 on the same axes, and (c) give the domain and the range of f and f^-1. If the function is not one-to-one, say so.

a. y = 4x - 5

b. y = 4/x, x ≠0

4. Graph each function.

a. f(x) = (1/4)x

b. f(x) = 2^-|x|

5. Solve each equation.

a. (2/3)^x = (9/4)

b. x^2/5 = 16

6. Future value-Find the future value and interest earned if $56,780 is invested at 5.3% compounded quarterly for 23 quarters.

7. Interest rate-Find the required annual interest rate to the nearest tenth of a percent for $65,000 to grow to $65,325 if interest is compounded monthly for 6 months.

8. If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form.

a. 2⁵ = 32

b. Log₄(1/64) = -3

9. Solve each logarithmic equation.

a. x = log₃(1/81)

b. x = log₅⁴√25

10. Use the properties of logarithms to rewrite the expression. Simplify the result if possible.

log₂(2√3 / 5)

11. Given the approximationslog10 2 = 0.3010 and lo10 3 = 0.4771 , find each logarithm without using a calculator.

log₁₀(20/27)

12. Find each value. If applicable, give an approximation to four decimal places.

a. log 10⁷

b. log 0.01

c. log 0.0055

13. Earthquake intensity-On December 26, 2004, an earthquake struck the Indian Ocean with a magnitude of 9.1 on the Richter scale. The resulting tsunami killed an estimated 229,900 people in several countries. Express this reading in terms of I0.

14. Use the change-of-base theorem to find an approximation to four decimal places for each logarithm.

log₂ 9

15. Solve each exponential equation. Express irrational solutions as decimals correct to the nearest thousandth.

a. (1/3)^x = 6

b. 5(1.2)^3x-2 + 1 = 7

16. Solve the following logarithmic equation. Express the solution in exact form.

In (2x) = 5

17. Investment time-Find t to the nearest hundredth year if $1786 becomes $2063 at 2.6%, with interest compounded monthly.

A = P[1 + (r/n)]^tn and A = Pe^rt

18. Interest rate-At what interest rate, to the nearest hundredth of a percent, will $16,000 grow to 20,000 if invested for 5.25 yr and interest is compounded quarterly.

A = P[1 + (r/n)]^tn and A = Pe^rt

19. Carbon-14 dating-A sample from a refuse deposit near the Strait of Magellan had 60% of the carbon-14 of a contemporary sample. How old was the sample

20. Dissolving a chemical-The amount of a chemical that will dissolve in a solution increases exponentially as the (Celsius) temperature t is increased according to the model A(t) = 10e^0.095t At what temperature will 15g dissolve?

21. Growth of an account-Russ McClelland, who is self-employed, wants to invest $60,000 in a pension plan. One investment offers 5% compounded quarterly. Another offers 4.75% compounded continuously. If Russ chooses the plan with continuous compounding, how long will it take for his $60,000 to grow to $80,000?

22. Doubling time-If interest is compounded continuously and the interest rate is tripled, what effect will this have on the time required for an investment to double?