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{\Large TEST 3

Math 1090 - 2}
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You have 50 minutes to complete the test.
Show all relevant work (or else no credit).  
Make your work legible, if I can't read it, I can't grade it.  
Each problem is worth 10 points.
Use the back of the pages if necessary.
You will be graded on clarity of answers.
{\bf A correct answer with incorrect or no work is worth no points.}
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Name \rule{5in}{.2pt}

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\begin{enumerate}

\item  \label{vw1}
You spend some time researching VW camper vans and 
studying their acceleration.
You test the following model:
The time $t$, in \emph{minutes}, that it takes a Volkswagen camper van
to accelerate to $x$ miles per hour can be modeled by the equation:
\[
t = .01(-597.62+.1976x^2 +21.017x)
\]
How fast can the camper van go after 11 minutes?
(Your answer may not reflect the acceleration in your car, 
but remember that this is a VW.)

\item  You have a business and you model the number of 
employees you have by the equation
\[
N=-.23t^2+4.89t+52.12
\]
where $t$ is the number of years past $1999$ and $N$ is the number of employees.
Do you have a maximum or minimum number of employees.
When does this happen, and how many employees? 
(Write it in a good sentence!!!)

Extra credit-2 points:  When does your business die how do you know it dies then?

\item  
\begin{enumerate}
\item  Write the following equation in logarithm form
\[
5^{-3}=\frac{1}{125}
\]
\item  Write the following equation in exponential form
\[
\log_3 \frac{1}{9}=-2
\]
\end{enumerate}

\item  Get a decimal approximation of $\log_2 10$, 
and check your answer using exponentials. (Show your work.)

\item The length $x$, in centimeters, of brook trout is modeled by the equation
\[
x=60-50e^{-.05t}
\]
where $t$ is the age of the fish in months.
You catch a 55~cm trophy brook trout.
How old is it?  (Answer in sentences!!)

\item  Volkswagen camper owners have found that the more stickers on their buses,
the more likely they are to be pulled over by the police and illegally searched.
It is somehow determined that if you drive your VW bus from coast to coast, 
with $x$ stickers on your bus, the chance $P$, in percentage,
that you will be pulled over and illegally searched at least once is
\[
P=90 (.12)^{.91^x}
\]
\begin{enumerate}
\item  What is your chance of being illegally searched with no stickers on your bus?
(Sentences!!)
\item  How many stickers can you have on your bus if you are willing to accept a 
$30\%$ risk of being illegally searched.
(I'll give you 1 point extra credit if you also have the exact answer, no decimals.
In either case, you do need the decimal answer.)
(Sentences!!)
\end{enumerate}

\end{enumerate}

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