MATH 2070
Fall 2016
Test 2 (Sections 5.7, 5.8, & 6.1 – 6.4)
Version A
Multiple Choice: Use a #2 pencil and completely fill in each bubble on your scantron to indicate the
answer to each question. Each question has one correct answer. If you indicate more than one
answer, or leave a blank, the question will be marked as incorrect. In this section there are 16
multiple choice questions. Each question is worth 3 points for a total of 48 points. For future
reference, circle your answers on this test paper as you will not receive your Scantron back with
your test.
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Haydrian purchased a 10 year franchise for a pizza store that is expected to generate profits at a rate
of R(t )  30000 dollars per year for the next 10 years. Haydrian plans to invest all of his profits into
an account that offers 2.5% interest compounded continuously. Assume a continuous income stream.
Use this information to answer the next three questions.
1. How much money will be in Haydrian’s account at the end of the 10-year investment period?
a. $233,640.23
b. $265,439.06
c. $340,830.50
d. $385,207.63
2. What is the 10-year present value of Haydrian’s investment?
a. $233,640.23
b. $265,439.06
c. $292,592.97
d. $385,207.63
3. How much interest will be in Haydrian’s account at the end of the 10-year investment period?
a. $34,560.94
b. $40,830.50
c. $75,391.44
d. $34,083.05
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MATH 2070
Test 2 (Sections 5.7, 5.8, & 6.1 – 6.4)
Fall 2016
Version A
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The daily quantity of 3-lb bags of fresh oranges consumers will demand and producers will supply
in a large city can be modeled as
0.076 p 2  0.123 p  2.422 when p  1.75
D ( p )  0.05 p 2  0.82 p  6.448 and S ( p )  
0
when p  1.75

thousand bags when p dollars per bag is the price of a 3-lb bag.
Check: D(5)  1.098 and S (5)  3.707
Use this information to answer the next four questions.
4. What is the consumer expenditure when 2 thousand bags are purchased?
a. 8.6 thousand dollars
b. 4.3 thousand dollars
c. 4.96 thousand dollars
d. 5.81 thousand dollars
5. How many 3-lb bags of oranges are produced when a bag is sold for $3.50?
a. 2.923 thousand
b. 2.966 thousand
c. 3.034 thousand
d. 4.661 thousand
6. Find the producer surplus when a 3-lb bag of oranges is sold for $3.50.
a. 1.627 thousand dollars
b. 1.413 thousand dollars
c. 6.892 thousand dollars
d. 4.624 thousand dollars
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MATH 2070
Fall 2016
Test 2 (Sections 5.7, 5.8, & 6.1 – 6.4)
Version A
 context continued
7. Which of the following shaded regions represents the consumer willingness and ability to spend
at market equilibrium?
a.
b.
c.
d.
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8. Evaluate the expression: lim 5e3 N  lim 5e3(2) .
N 
N 
a. 
b. 5e6
c. 
d. 5e6
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MATH 2070
Test 2 (Sections 5.7, 5.8, & 6.1 – 6.4)
Fall 2016
Version A
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3
9. Which of the following is equivalent to

f '( x )dx ?

a.  lim f '( N )    lim f '(3) 
 N 
  N 

b.  lim f ( N )    lim f (3) 
 N 
  N 

c.  lim f '(3)    lim f '( N ) 
 N 
  N 

d.  lim f (3)    lim f ( N ) 
 N 
  N 

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A company’s profit between 1990 and 2010 can be modeled by P (t )  0.2t 3  4.125t 2  2t  56
million dollars where t is the number of years since 1990.
Check: P(3)  93.725
Use this information to answer the next two questions.
10. What was the company’s average profit between 2000 and 2010?
a. 2985 million dollars
b. 1535 million dollars
c. 298.5 million dollars
d. 153.5 million dollars
11. On average, how quickly was the company’s profit changing between 1990 and 1995?
a. 17.625 million dollars per year
b. 88.125 million dollars per year
c. 89.125 million dollars per year
d. 132.925 million dollars per year
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MATH 2070
Test 2 (Sections 5.7, 5.8, & 6.1 – 6.4)
Fall 2016
Version A
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The rate of change of a company’s revenue is modeled by r ( x )  0.5 x3  3 x thousand dollars per
year and the rate of change of the same company’s cost is c( x)  e 0.5 x thousand dollars per year,
where x is the number of years since 2010. The areas trapped between the two curves are labeled as
A1, A2, and A3.
Check: r (2)  2 and c(2)  2.718
Use this information to answer the next two questions.
12. Find A1.
a. 0.201
b. 0.207
c. 0.718
d. 0.723
13. Which of the following is the correct interpretation of A1 ?
a. The company’s profit decreased an average of A1 thousand dollars per year during this
time.
b. The company’s profit increased an average of A1 thousand dollars per year during this
time.
c. The company’s profit increased by A1 thousand dollars during this time.
d. The company’s profit decreased by A1 thousand dollars during this time.
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MATH 2070
Test 2 (Sections 5.7, 5.8, & 6.1 – 6.4)
Fall 2016
Version A
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A quantity of a certain isotope is known to decay at a rate of r (t )  0.012(0.9998t ) mgs per year,
Check: r (5)  0.011988
where t is the number of years since the isotope started to decay.
Use this information to answer the next two questions.
14. Eventually, how much of the isotope will decay?
a. 59.994 mgs
b. 51.876 mgs
c. 1.062 mgs
d. 60.257 mgs
5000

15. Which of the following is the correct interpretation of
r (t )dt
0
5000
 0.008 ?
During the first five thousand years …
a.
… the isotope decayed at a rate of 0.008 mgs per year.
b.
… the isotope decayed by an average of 0.008 mgs per year.
c.
…the average mass of the isotope decreased by 0.008 mgs per year.
d.
…the rate of decay of the isotope decreased by an average of 0.008 mgs per year.
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Last year, a corporation had a profit of $29 million. They expect their profits to increase by $3.4
million each year over the next five years. Assume that the corporation will begin investing all of
their profits into an account for which interest is compounded continuously at a rate of 1.9%.
Assume a continuous income stream.
16. Which of the following is the correct income stream function for this situation?
a. R(t )  0.019(29(1.034t )) million $ per year
b. R (t )  0.019  29  3.4t  million $ per year
c. R(t )  29  3.4t million $ per year
d. R (t )  29(1.019 t )  3.4 million $ per year
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Check your Scantron now to make sure it will successfully run. If it does, you will earn one point.
When you are not working on the multiple choice portion of the test, turn your Scantron over
so that it cannot be read by others in the room.
10
MATH 2070
Fall 2016
Test 2 (Sections 5.7, 5.8, & 6.1 – 6.4)
Version A
Free Response: RE-READ the directions at the beginning of the test. Then read each question
carefully. Provide only one clearly indicated answer to each question. If your answer is illegible, it
will be graded as incorrect. Show all work. The free response portion is 51% of your test grade.
For each question, set up the specific mathematical notation that is being evaluated to obtain your
answer. No credit will be awarded for simply copying generic formulas from the formula sheet.
Little or no credit will be awarded for answers without the corresponding notation.
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1. The amount of carbon dioxide in the atmosphere
from 1750 to 2000 be modeled by C (t )  280e0.00119 t
parts per million, t years since 1750.
Check: C (5)  281.671
250
 C(t )dt
a. Find
0
250
and give your answer in a sentence of interpretation.
(5 pts)
b. When was the amount of carbon dioxide in the atmosphere equal to the average amount of
carbon dioxide in the atmosphere between 1750 and 2000? Round to three decimal places.
t = ________________________ years since 1750
(3 pts)
c. Which of the following expressions could be evaluated to find the average rate of change in
the amount of carbon dioxide in the atmosphere between 1750 and 2000? Circle all that apply.
(3 pts)
250
250
C (t )dt
0
0 C '(t )dt
C (250)  C (0)
C '(250)  C '(0)
250
250
250
250
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MATH 2070
Test 2 (Sections 5.7, 5.8, & 6.1 – 6.4)
Fall 2016
Version A
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2. The monetary value of a certain antique chair increases with its age (but at a diminishing rate).
1400
The rate of change in the value of the chair can be modeled as v( x)  1.5 dollars per year
x
where x years is the age of the chair, x  16 . The chair was valued at $200 sixteen years after it
was crafted.
Use the algebraic method to determine how much the chair eventually will be worth. Show all
of your steps and use proper notation throughout your work.
(9 pts)

1400
dx 
1.5
16 x

Conclusion: The chair eventually will be worth ______________________ dollars.
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MATH 2070
Test 2 (Sections 5.7, 5.8, & 6.1 – 6.4)
Fall 2016
Version A
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3. Suppose that the weekly demand and supply for organic butter can be modeled by
D( p)  15000 1200 p thousand pounds and
0
thousand pounds when p  2.49

S ( p)  
2
467 p  460 p  267.4752 thousand pounds when p  2.49
when $p per pound is the price of organic butter.
Check: D(3)  11400 and S (3)  3090.4752
a. What is the shutdown price for a pound
of organic butter?
(3 pts)
__________________ dollars per pound
b. What is the price above which consumers will no longer demand organic butter? Round to two
decimal places.
(3 pts)
__________________ dollars per pound
c. Find the price at the point of unit elasticity. Show work. Round to two decimal places and
include units.
(4 pts)
d. Find the point of market equilibrium.
p*  ______________________________
(round to two places and include units)
(4 pts)
q*  _________________________________
(include units)
e. Find the total social gain at market equilibrium. Show work. Round to three decimal places and
include units.
(6 pts)
problem continues 
13
MATH 2070
Fall 2016
Test 2 (Sections 5.7, 5.8, & 6.1 – 6.4)
Version A
f. Find the total area of the shaded region between
p = 6 and p = 10.
Show work. Round your answer to three decimal
places. Units are not necessary.
(4 pts)
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4. A company showed a profit of $1.2 million last year. The CEO of the company expects the
profit to decrease by 6% each year over the next five years and half of the profits will be
continuously invested into an account bearing a 2.75% interest rate where the interest is
compounded continuously.
a. Write the income flow rate, R(t), of the income stream. Include units.
(4 pts)
R(t) 
b. Set up the specific notation that would be evaluated to determine how much money will be
in the account at the end of the five year investment period. You do not need to find this
amount.
(3 pts)
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Did you set up specific, mathematical notation throughout the free response section?
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