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{\Large TEST 6

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.
Use correct English sentences where necessary for full credit!
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Name \rule{5in}{.2pt}

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\begin{enumerate}

\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?  (Sentences!!)
(I'll give you 1 point extra credit if you have the exact answer too.)

\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.)
(Sentences!!)
\end{enumerate}


\end{enumerate}

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