Answer all 22 exercises, and show all work in this word document
Answer all 22 exercises, and show all work in this word document. An asterisk indicates an exercise for which a graph needs to be provided, #3 and #4.
1. Decide whether each function as graphed or defined is one-to-one. (See section 4.1, Examples 1 and 2.) [9 points]
2. Use the definition of inverses to determine whether f and g are inverses. (See section 4.1, Example 3.) [3 points]
3. For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form (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. (See section 4.1, Examples 5–8.) [6 points]
4. Graph each function.* (See section 4.2, Example 2.) [6 points]
5. Solve each equation. (See section 4.2, Examples 4–6.) [6 points]
6. Future value—Find the future value and interest earned if $56,780 is invested at 5.3% compounded quarterly for 23 quarters. (See section 4.2, Examples 7–9.) [3 points]
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.(See section 4.2, Examples 7–9.) [3 points]
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. (See section 4.3, Example 1.) [6 points]
a.
b.
9. Solve each logarithmic equation. (See section 4.3, Example 2.) [6 points]
a.
b.
10. Use the properties of logarithms to rewrite the expression. Simplify the result if possible. (See section 4.3, Example 5.) [3 points]
11. Given the approximations and
, find each logarithm without using a calculator. (See section 4.3, Example 7.) [3 points]
12. Find each value. If applicable, give an approximation to four decimal places. (See section 4.4, Example 1.) [9 points]
a.
b.
c.
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. (See section 4.4, Example 4.) [3 points]
14. Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. (See section 4.4, Example 8.) [3 points]
15. Solve each exponential equation. Express irrational solutions as decimals correct to the nearest thousandth. (See section 4.5, Examples 1–4.) [6 points]
a.
b.
16. Solve the following logarithmic equation. Express the solution in exact form. (See section 4.5, Examples 5–9.) [3 points]
17. Investment time—Find t to the nearest hundredth year if $1786 becomes $2063 at 2.6%, with interest compounded monthly. Refer to the formulas for compound interest
and
from section 4.2 [3 points]
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. Refer to the formulas for compound interest
and
from section 4.2 [3 points]
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? (See section 4.6, Example 5.) [4 points]
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 At what temperature will 15g dissolve? [4 points]
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? [4 points]
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? (See section 4.6, Example 2.) [4 points]
