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. x2/5 = 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 = Pert
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 = Pert
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) = 10e0.095t 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?