Question 1

Find the associated exponential decay model.   $Q = 7,000$ when $t = 0$ ; Half-life = 9

Accepted Answer

A)  $Q = 7,000 - e ^ { - \frac { t } { 9 } }$ 
B)  $Q = 7,000 e ^ { - \frac { t ( \ln 2 ) } { 9 } }$ 
C)  $Q = 7,000 + e ^ { \frac { t ( \ln 2 ) } { 9 } }$ 
D)  $Q = 7,000 e ^ { - \frac { t } { 9 } }$ 
E)  $Q = 7,000 e ^ { \frac { t } { 9 } }$ 
A)  $Q = 7,000 - e ^ { - \frac { t } { 9 } }$ 
B)  $Q = 7,000 e ^ { - \frac { t ( \ln 2 ) } { 9 } }$ 
C)  $Q = 7,000 + e ^ { \frac { t ( \ln 2 ) } { 9 } }$ 
D)  $Q = 7,000 e ^ { - \frac { t } { 9 } }$ 
E)  $Q = 7,000 e ^ { \frac { t } { 9 } }$

Question 2

How long, to the nearest year, will it take an investment to triple if it is continuously compounded at 15% per year 
 
Round the answer to the nearest year.
 
__________ years

Accepted Answer

The answer of How long, to the nearest year, will...

Question 3

Given the graph of the functions $f _ { 1 } ( x ) = 2.3 ^ { - x }$ and $f _ { 2 } ( x ) = e ^ { - x }$ . Determine the color of the graph that corresponds to $f _ { 1 } ( x )$ .      
Select the correct answer.

Accepted Answer

A) Blue 
B)  Red 
A) Blue 
B)  Red

Question 4

For the following demand equation, find the largest possible revenue.  
 $q = - 4 p + 3,600$

Accepted Answer

A) 1,620,000 
B)   450 
C)   900 
D)   810,000 
E)   648,000 
A) 1,620,000 
B)   450 
C)   900 
D)   810,000 
E)   648,000

Question 5

You are the sales manager for Montevideo Productions, Inc., and you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,500. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 35 contracts. This is down 10 contracts from the figure last year, when your company charged only $2,000. Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo Productions, Inc., charges for development.

Accepted Answer

A)  $q = - 50 p - 85$ 
B)    $q = - 0.02 p - 85$ 
C)   $q = - 0.02 p + 85$ 
D)   $q = 50 p + 85$ 
E)   $q = 0.02 p + 85$ 
A)  $q = - 50 p - 85$ 
B)    $q = - 0.02 p - 85$ 
C)   $q = - 0.02 p + 85$ 
D)   $q = 50 p + 85$ 
E)   $q = 0.02 p + 85$

Question 6

The table lists interest rates on long-term investments (based on 10-year government bonds) in several countries in 2004-2005. Assuming that you invest $13,000 in Japan, how long (to the nearest year) must you wait before your investment is worth $19,000 if the interest is compounded annually  Round your answer to the nearest year. $$\begin{array} { | l | l | l | l | } 
\hline \text { Country } & \text { U.S. } & \text { Japan } & \text { Canada } \
\hline \text { Yield } & 5.3 \% & 1.5 \% & 5.2 \% \
\hline
\end{array}$$

Accepted Answer

A) 26 years 
B)  19 years 
C)  25 years 
D)  22 years 
E)  28 years 
A) 26 years 
B)  19 years 
C)  25 years 
D)  22 years 
E)  28 years

Question 7

Graph the function.   $f ( x ) = \log _ { 5 } x$

Accepted Answer

A)    
B)      
C)      
D)      
E)     
A)    
B)      
C)      
D)      
E)

Question 8

Suppose the amount of carbon dioxide (in pounds per 15,000 miles) released by a typical sport utility vehicle (SUV) depends on its fuel efficiency according to the formula  
 $10 x ^ { 2 } - 580 x + 30,803$  
Where x is a fuel efficiency of an SUV in miles per gallon. According to the model, what is the fuel efficiency of an SUV that has the least carbon dioxide pollution

Accepted Answer

A) 14 miles per gallon 
B)  19 miles per gallon 
C)  18 miles per gallon 
D)  32 miles per gallon 
E)  29 miles per gallon 
A) 14 miles per gallon 
B)  19 miles per gallon 
C)  18 miles per gallon 
D)  32 miles per gallon 
E)  29 miles per gallon

Question 9

Choose the correct letter for each question.
​
--5

Accepted Answer

A) $x ^ { 2 } - 6 x + 8$ 
B) $x ^ { 2 } + 10 x + 25$ 
C) $x ^ { 2 } + 10 x + 30$ 
A) $x ^ { 2 } - 6 x + 8$ 
B) $x ^ { 2 } + 10 x + 25$ 
C) $x ^ { 2 } + 10 x + 30$

Question 10

Graph the function.   $f ( x ) = \log _ { \frac { 1 } { 6 } } x$

Accepted Answer

A)     
B)      
C)     
D)     
E)     
A)     
B)      
C)     
D)     
E)

Question 11

Soon after taking an aspirin, a patient has absorbed 310 mg of the drug. If the amount of aspirin in the bloodstream decays exponentially with half being removed every 2 hours, find the amount of aspirin in the bloodstream after 9 hours. ​
Select the correct answer.
​

Accepted Answer

A) 1,370 
B)  137 
C)  50 
D)  13.7 
E)  2.21 
A) 1,370 
B)  137 
C)  50 
D)  13.7 
E)  2.21

Question 12

Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crowding and smaller lot sizes. In fact, if the company builds 60 houses in this particular development, it can sell them for $160,000 each, but if it builds 70 houses, it will be able to get only $150,000 each. What is the largest possible revenue the company can get  Round your answer to the nearest dollar. ?

Accepted Answer

A) $11,000,000 
B)  ?$11,856,000 
C)  ?$363,000 
D)  ?$12,100,000 
E)  ?$12,226,000 
A) $11,000,000 
B)  ?$11,856,000 
C)  ?$363,000 
D)  ?$12,100,000 
E)  ?$12,226,000

Find the associated exponential decay model. $Q = 7,000$ when $t = 0$ ; Half-life = 9

How long, to the nearest year, will it take an investment to triple if it is continuously compounded at 15% per year Round the answer to the nearest year. __________ years

For the following demand equation, find the largest possible revenue. $q = - 4 p + 3,600$

Graph the function. $f ( x ) = \log _ { 5 } x$

Choose the correct letter for each question. --5

Graph the function. $f ( x ) = \log _ { \frac { 1 } { 6 } } x$

Soon after taking an aspirin, a patient has absorbed 310 mg of the drug. If the amount of aspirin in the bloodstream decays exponentially with half being removed every 2 hours, find the amount of aspirin in the bloodstream after 9 hours. Select the correct answer.

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Exam 2: Nonlinear Functions and Models

Find the associated exponential decay model. Q=7,000Q = 7,000Q=7,000 when t=0t = 0t=0 ; Half-life = 9