5.5 Bases other than e and Applications 321
5.5 Bases other than e and Applications
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Evaluate the following expression without using a calculator.
a.
b.
c. –12
d. 64
e.
____ 2. Solve each of the following equations for .
a.
b.
c.
d.
e.
____ 3. Solve each of the following equations for .
a.
b.
c.
d.
e.
322 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
____ 4. Solve the following equation for .
a.
b.
c.
d. 3
e.
____ 5. Solve the following equation for .
a.
b.
c.
d.
e.
____ 6. Solve the following equation for .
a.
b.
c.
d.
e.
____ 7. Find if .
a.
b.
c.
d.
e.
5.5 Bases other than e and Applications 323
____ 8. Find if .
a.
b.
c.
d.
e.
____ 9. Find if .
a.
b.
c.
d.
e.
324 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
____ 10. Find if .
a.
b.
c.
d.
e.
____ 11. Find an equation of the tangent line to the graph of at the point .
a.
b.
c.
d.
e.
____ 12. Find an equation of the tangent line to the graph of at the point .
a.
b.
c.
d.
e.
5.5 Bases other than e and Applications 325
____ 13. Use logarithmic differentiation to find .
a.
b.
c.
d.
e.
____ 14. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 15. Find the following indefinite integral.
a.
b.
c.
d.
e.
326 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
____ 16. If the annual rate of inflation averages over the next years, the approximate
cost of goods or services during any year in that decade is where is the time in
years and is the present cost. The price of an oil change for your car is presently . Estimate
the price years from now. Round your answer to two decimal places.
a. $26.30
b. $30.67
c. $78.89
d. $25.61
e. $94.31
____ 17. If the annual rate of inflation averages over the next years, the approximate
cost of goods or services during any year in that decade is where is the time in
years and is the present cost. The price of an oil change for your car is presently . Find the
rate of change of with respect to when . Round your answer to three decimal places.
a. 32.176 dollars per year
b. 1.966 dollars per year
c. 2.293 dollars per year
d. 5.962 dollars per year
e. 32.730 dollars per year
____ 18. Suppose that was invested at an annual rate of percent compounded
times per year. Determine the balance in the account after years for each of the following values of
( corresponds to continuous compounding of interest).
a.
b.
c.
d.
e.
____ 19. Determine the balance of an account after 25 years where and
compounded continuously. Round your answer to the nearest cent.
a. $28,773.01
b. $14,386.51
c. $5,997.19
d. $7,095.34
e. $82,788.63
5.5 Bases other than e and Applications 327
____ 20. The yield V (in millions of cubic feet per acre) for a stand of timber at age t is
V = 6.8e(–47.6) / t where t is measured in years. Find the limiting volume of wood per acre as t
approaches infinity. Round your answer to one decimal place.
a. 9.5 million ft3/acre
b. 4.8 million ft3/acre
c. 18.5 million ft3/acre
d. 18.3 million ft3/acre
e. 6.8 million ft3/acre
____ 21. The yield V (in millions of cubic feet per acre) for a stand of timber at age t is
V = 5.9e(–48.8) / t where t is measured in years. Find the rates at which the yield is changing when
t = 60 years. Round your answer to three decimal places.
a. 0.035 (million ft3/acre)/year
b. 0.044 (million ft3/acre)/year
c. 0.079 (million ft3/acre)/year
d. 0.053 (million ft3/acre)/year
e. 0.016 (million ft3/acre)/year
____ 22. A lake is stocked with fish, and their population increases according to the
logistic curve where t is measured in months. At what rate is the fish population
changing at the end of 3 months? Round your answer to one decimal place.
a. 79.9 fish per month
b. 126.6 fish per month
c. 253.2 fish per month
d. 123.9 fish per month
e. 159.7 fish per month
328 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
5.5 Bases other than e and Applications – Answer Section