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MAT 121 Chapter 5 Test



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

Evaluate the expression.

mc001-1.jpg
A
3
B
2
C
27
D
24
 

 2. 

Evaluate the expression.

mc002-1.jpg
A
mc002-2.jpg
B
mc002-3.jpg
C
mc002-4.jpg
D
mc002-5.jpg
E
mc002-6.jpg
 

 3. 

Simplify the expression.

mc003-1.jpg
A
mc003-2.jpg
B
mc003-3.jpg
C
mc003-4.jpg
D
mc003-5.jpg
E
mc003-6.jpg
 

 4. 

Simplify the expression.

mc004-1.jpg
A
mc004-2.jpg
B
mc004-3.jpg
C
mc004-4.jpg
D
mc004-5.jpg
 

 5. 

Solve the equation for x.

mc005-1.jpg
A
x  =  2
B
x =  16
C
x  =  8
D
x  =  7
 

 6. 

Solve the equation for x.

mc006-1.jpg
A
mc006-2.jpg
B
mc006-3.jpg
C
mc006-4.jpg
D
mc006-5.jpg
E
mc006-6.jpg
 

 7. 

Solve the equation for x.

mc007-1.jpg
A
mc007-2.jpg
B
mc007-3.jpg
C
mc007-4.jpg
D
mc007-5.jpg
 

 8. 

Sketch the graphs of the given functions on the same axes.

mc008-1.jpg
A
mc008-2.jpg
C
mc008-4.jpg
B
mc008-3.jpg
 

 9. 

Sketch the graphs of the given functions on the same axes.

mc009-1.jpg
A
mc009-2.jpg
C
mc009-4.jpg
B
mc009-3.jpg
 

 10. 

Sketch the graphs of the functions on the same axes.

mc010-1.jpg
A
mc010-2.jpg
D
mc010-5.jpg
B
mc010-3.jpg
E
mc010-6.jpg
C
mc010-4.jpg
 

 11. 

The concentration of a drug in an organ at any time t (in seconds) is given by

mc011-1.jpg

where C(t) is measured in milligrams/cubic centimetermc011-2.jpg. What is the concentration to four decimal places of the drug in the organ after 15 sec?
A
mc011-3.jpg
B
mc011-4.jpg
C
mc011-5.jpg
D
mc011-6.jpg
 

 12. 

Express the equation in logarithmic form.

mc012-1.jpg
A
mc012-2.jpg
B
mc012-3.jpg
C
mc012-4.jpg
D
mc012-5.jpg
 

 13. 

Express the equation in logarithmic form.

mc013-1.jpg
A
mc013-2.jpg
B
mc013-3.jpg
C
mc013-4.jpg
D
mc013-5.jpg
 

 14. 

Sketch the graph of the equation.

mc014-1.jpg
A
mc014-2.jpg
D
mc014-5.jpg
B
mc014-3.jpg
E
mc014-6.jpg
C
mc014-4.jpg
 

 15. 

Use logarithms to solve the equation for t. Round your answer to four decimal places.

mc015-1.jpg
A
mc015-2.jpg
B
mc015-3.jpg
C
mc015-4.jpg
D
mc015-5.jpg
 

 16. 

Use logarithms to solve the equation for t.

mc016-1.jpg
A
mc016-2.jpg
B
mc016-3.jpg
C
mc016-4.jpg
D
mc016-5.jpg
 

 17. 

Use logarithms to solve the equation for t. Please round the answer to four decimal places.

mc017-1.jpg
A
mc017-2.jpg
B
mc017-3.jpg
C
mc017-4.jpg
D
mc017-5.jpg
E
mc017-6.jpg
 

 18. 

The height (in feet) of a certain kind of tree is approximated by mc018-1.jpg  where mc018-2.jpg is the age of the tree in years. Estimate the age of an 70-ft tree. Round your answer to the nearest hundredth.
A
17.53 years
B
16.69 years
C
16.10 years
D
19.70 years
 

 19. 

The concentration of a drug in an organ at any time t (in seconds) is given by  mc019-1.jpg   where mc019-2.jpg is measured in grams/cubic centimeter mc019-3.jpg. How long would it take for the concentration of the drug in the organ to reach 0.18mc019-4.jpg?

Please round the answer to two decimal places.
A
mc019-5.jpg sec
B
mc019-6.jpg sec
C
mc019-7.jpg sec
D
mc019-8.jpg sec
E
mc019-9.jpg sec
 

 20. 

Use the definition of a logarithm to prove mc020-1.jpg.
A
By the definition mc020-2.jpg means mc020-3.jpg.
B
By the definition mc020-4.jpg means mc020-5.jpg.
C
By the definition mc020-6.jpg means mc020-7.jpg.
 

 21. 

Find the accumulated amount after 3 year(s) if $6,000 is invested at 8% compounded continuously.
A
$7,609.45
B
$7,621.42
C
$7,591.91
D
$7,627.49
 

 22. 

Find the interest rate needed for an investment of $5,000 to grow to an amount of $7,000 in 4 year(s) if interest is compounded continuously.
A
8.55% per year
B
8.69% per year
C
8.41% per year
D
8.62% per year
E
8.48% per year
 

 23. 

How long will it take an investment of $7,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to two decimal places.
A
mc023-1.jpg year(s)
B
mc023-2.jpg year(s)
C
mc023-3.jpg year(s)
D
mc023-4.jpg year(s)
E
mc023-5.jpg year(s)
 

 24. 

Find the present value of $57,939 due in 6 year(s) at an interest rate of 9% / year compounded continuously. Round your answer to the nearest integer.
A
$33,764
B
$34,165
C
$33,766
D
$34,547
 

 25. 

A condominium complex was purchased by a group of private investors for $1.5 million and sold 5 year(s) later for $3.7 million. Find the annual rate of return (compounded continuously) on their investment.
A
18.90%
B
18.47%
C
18.06%
D
18.19%
 

 26. 

Find the derivative of the function.

mc026-1.jpg
A
mc026-2.jpg
B
mc026-3.jpg
C
mc026-4.jpg
D
mc026-5.jpg
 

 27. 

Find the derivative of the function.

mc027-1.jpg
A
mc027-2.jpg
B
mc027-3.jpg
C
mc027-4.jpg
D
mc027-5.jpg
 

 28. 

Find the derivative of the function.

mc028-1.jpg
A
mc028-2.jpg
B
mc028-3.jpg
C
mc028-4.jpg
D
mc028-5.jpg
 

 29. 

Find the derivative of the function.

mc029-1.jpg
A
mc029-2.jpg
B
mc029-3.jpg
C
mc029-4.jpg
D
mc029-5.jpg
 

 30. 

Find the derivative of the function.

mc030-1.jpg
A
mc030-2.jpg
B
mc030-3.jpg
C
mc030-4.jpg
D
mc030-5.jpg
 

 31. 

Find the derivative of the function.

mc031-1.jpg
A
mc031-2.jpg
B
mc031-3.jpg
C
mc031-4.jpg
D
mc031-5.jpg
 

 32. 

Find the derivative of the function.

mc032-1.jpg
A
mc032-2.jpg
B
mc032-3.jpg
C
mc032-4.jpg
D
mc032-5.jpg
E
mc032-6.jpg
 

 33. 

Find the second derivative of the function.

mc033-1.jpg
A
mc033-2.jpg
B
mc033-3.jpg
C
mc033-4.jpg
D
mc033-5.jpg
 

 34. 

Determine the intervals where the function mc034-1.jpg is decreasing.
A
mc034-2.jpg
B
mc034-3.jpg
C
mc034-4.jpg
D
mc034-5.jpg
 

 35. 

Determine the intervals of concavity for the function.

mc035-1.jpg
A
Concave downward on mc035-2.jpg
Concave upward on mc035-3.jpg
B
Concave downward on mc035-4.jpg
Concave upward on mc035-5.jpg
C
Concave downward on mc035-6.jpg
D
Concave downward on mc035-7.jpg
Concave upward on mc035-8.jpg
E
Concave downward on mc035-9.jpg
Concave upward on mc035-10.jpg
 

 36. 

Use the curve-sketching guideline, to select the graph of the function.

mc036-1.jpg
A
mc036-2.jpg
C
mc036-4.jpg
B
mc036-3.jpg
 

 37. 

Based on data obtained from the Census Bureau, the manager of Plymouth Van Lines estimates that the percent of the total population relocating in year t ( mc037-1.jpg corresponds to the year 1960) may be approximated by the formula  mc037-2.jpg.

Compute mc037-3.jpg, mc037-4.jpg, and mc037-5.jpg.
A
mc037-6.jpg
mc037-7.jpg
mc037-8.jpg
B
mc037-9.jpg
mc037-10.jpg
mc037-11.jpg
C
mc037-12.jpg
mc037-13.jpg
mc037-14.jpg
D
mc037-15.jpg
mc037-16.jpg
mc037-17.jpg
E
mc037-18.jpg
mc037-19.jpg
mc037-20.jpg
 

 38. 

The monthly demand for a certain brand of perfume is given by the demand equation mc038-1.jpg   where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when  x =  1,000.
A
The rate of change of the price is - 2.22 cents per bottle.
B
The rate of change of the price is - 3.62 cents per bottle.
C
The rate of change of the price is - 2.62 cents per bottle.
D
The rate of change of the price is 5.24 cents per bottle.
 

 39. 

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by

mc039-1.jpg .

How fast is the price of the commodity changing at mc039-2.jpg?
A
Increasing at the rate of $14/wk.
B
Increasing at the rate of $19/wk.
C
Increasing at the rate of $5/wk.
D
Decreasing at the rate of $19/wk.
E
Decreasing at the rate of $14/wk.
 

 40. 

Find the derivative of the function.

mc040-1.jpg
A
mc040-2.jpg
B
mc040-3.jpg
C
mc040-4.jpg
D
mc040-5.jpg
 

 41. 

Find the derivative of the function.

mc041-1.jpg
A
mc041-2.jpg
B
mc041-3.jpg
C
mc041-4.jpg
D
mc041-5.jpg
 

 42. 

Find the derivative of the function.

mc042-1.jpg
A
mc042-2.jpg
B
mc042-3.jpg
C
mc042-4.jpg
D
mc042-5.jpg
 

 43. 

Find the derivative of the function.

mc043-1.jpg
A
mc043-2.jpg
B
mc043-3.jpg
C
mc043-4.jpg
D
mc043-5.jpg
 

 44. 

Find the derivative of the function.

mc044-1.jpg
A
mc044-2.jpg
B
mc044-3.jpg
C
mc044-4.jpg
D
mc044-5.jpg
 

 45. 

Find the derivative of the function.

mc045-1.jpg
A
mc045-2.jpg
B
mc045-3.jpg
C
mc045-4.jpg
D
mc045-5.jpg
 

 46. 

Find the derivative of the function.

mc046-1.jpg
A
mc046-2.jpg
B
mc046-3.jpg
C
mc046-4.jpg
D
mc046-5.jpg
 

 47. 

Find the second derivative of the function.

mc047-1.jpg
A
mc047-2.jpg
B
mc047-3.jpg
C
mc047-4.jpg
D
mc047-5.jpg
 

 48. 

Find an equation of the tangent line to the graph of mc048-1.jpg at the point mc048-2.jpg.
A
mc048-3.jpg
B
mc048-4.jpg
C
mc048-5.jpg
D
mc048-6.jpg
 

 49. 

Find the inflection points of the function mc049-1.jpg.
A
mc049-2.jpg
B
mc049-3.jpg
C
mc049-4.jpg
D
There are no inflection points.
 

 50. 

Find an equation of the tangent line to the graph of   mc050-1.jpg  at its inflection point.
A
mc050-2.jpg
B
mc050-3.jpg
C
mc050-4.jpg
D
mc050-5.jpg
E
mc050-6.jpg
 

 51. 

Given that a quantity Q(t) exhibiting exponential decay is described by the function
mc051-1.jpg  where t is measured in years. What is the decay constant? What quantity is present initially?

Complete the table of values. Round your answer to the nearest integer.

t
0
5
10
20
100
      
Q
____
____
____
____
____
      
A
k =  - 0.01;   Q  =  2,500
t      0         5        10        20        100 
Q      2,500     2,378    2,262     2,047     920
B
k  =  - 0.01;   Q  =  2,500
t      0        5        10        20        100 
Q      2,500    2,378    2,207     2,047     925
C
k  =  2,500;   Q  =  - 2,500
t     0         5        10        20        100  
Q     2,500     2,489    2,262     2,058     920
D
k  =  2,500;   Q  =  - 2,500
t     0          5        10       20        100 
Q     2,500     2,489    2,207     2,058     925

 

 52. 

A certain piece of machinery was purchased 4 year(s) ago by Garland Mills for $400,000. Its present resale value is $256,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 year(s) from now?
A
The resale value of the machinery will be $204,800
B
The resale value of the machinery will be $204,789
C
The resale value of the machinery will be $204,911
D
The resale value of the machinery will be $203,689
 

 53. 

The radioactive element polonium decays according to the law  mc053-1.jpg  where mc053-2.jpg is the initial amount and the time t is measured in days. If the amount of polonium left after 560 days is 40 mg, what was the initial amount present?
A
The initial amount was 642 mg
B
The initial amount was 629 mg
C
The initial amount was 635 mg
D
The initial amount was 640 mg
 

 54. 

Wood deposits recovered from an archeological site contain 25% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Hint: the decay constant k for carbon 14 is equal to 0.00012.
A
The tree died 13,084 year(s) ago.
B
The tree died 10,429 year(s) ago.
C
The tree died 8,096 year(s) ago.
D
The tree died 11,552 year(s) ago.
 

 55. 

The percent of a certain brand of computer chips that will fail after t years of use is estimated to be 

mc055-1.jpg.

What percent of this brand of computer chips are expected to be usable after 3 years?
A
52.6%
B
46.9%
C
45.5%
D
33.7%
 

 56. 

During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by  mc056-1.jpg.

How many children were stricken by the flu after the first day? How many children had the flu after 10 days? How many children eventually contracted the disease?
A
13 children were stricken by the flu after the first day; 1,264 children had the flu after 10 days; 883 children eventually contracted the disease
B
15 children were stricken by the flu after the first day; 1,125 children had the flu after 10 days; 1,354 children eventually contracted the disease
C
13 children were stricken by the flu after the first day; 1,125 children had the flu after 10 days; 1,200 children eventually contracted the disease
D
10 children were stricken by the flu after the first day; 1,264 children had the flu after 10 days; 1,200 children eventually contracted the disease
 

 57. 

Suppose a radioactive substance decays according to the formula  mc057-1.jpg.  How long will it take for the substance to decay to half the original amount?
A
It will take 5,281 years for the substance to decay to half the original amount.
B
It will take 5,170 years for the substance to decay to half the original amount.
C
It will take 5,626 years for the substance to decay to half the original amount.
D
It will take 40 years for the substance to decay to half the original amount.
 

Numeric Response
 

 58. 

Evaluate the expression.

nr058-1.jpg = __________

 

 59. 

Evaluate the expression.

nr059-1.jpg  =  __________

 

 60. 

Solve the equation for x.

nr060-1.jpg

nr060-2.jpg__________

 

 61. 

Find the present value of $58,669 due in 5 year(s) at an interest rate of 7% / year compounded continuously. Round your answer to the nearest dollar.

$__________

 

Short Answer
 

 62. 

Find the derivative of the function.

sa062-1.jpg
 

 63. 

Find the derivative of the function.

sa063-1.jpg
 

 64. 

Find the second derivative of the function.

sa064-1.jpg
 

 65. 

Find the derivative of the function.

sa065-1.jpg
 



 
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