Larson_Calculus_10e ch05sec05
MULTIPLE CHOICE
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.
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.
8. Find if .
a.
b.
c.
d.
e.
9. Find if .
a.
b.
c.
d.
e.
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.
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.
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
20. The yield (in millions of cubic feet per acre) for a stand of timber at age is
where is measured in years. Find the limiting volume of wood per acre as 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 (in millions of cubic feet per acre) for a stand of timber at age is
where is measured in years. Find the rates at which the yield is changing when 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 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