
\input graphicx
\nopagenumbers
\magnification 1400
\vsize 10.4truein
\voffset -.4truein
\parskip 20pt
\parindent 0pt
\hsize 7.3truein
\voffset -.4truein
%\hsize 10.2truein
\hoffset -.4truein
\def\R{{\bf R}}
\def\v{{\vskip 20pt}}

Quiz 2 Form A \hfil \break
Sept 15, 2016


[10] 1i.  Suppose \$75 is invested at an annual rate of return $r$ compounded continuously.
State the initial value problem describing the amount of money after $t$ years.

Differential equation:  $\underline{\hskip 3in}$ 

Initial Value:  $\underline{\hskip 3in}$ 

1ii. Circle the general solution to the differential equation in problem 1:

A.)  $y = ln|rt|+C$ \hfill 
B.)  $y = Cln|rt|$ \hfill 
C.)  $y = e^{rt}+C$ \hfill 
D.)  $y = Ce^{rt}$ \hfill 

1iii.  Circle the solution to the initial value problem in problem 1:

A.)  $y = ln|rt|+75$ \hfill 
B.)  $y = 75ln|rt|$ \hfill 
C.)  $y = e^{rt}+75$ \hfill 
D.)  $y = 75e^{rt}$ \hfill 



[10]~ 2.)  Suppose water containing 3 lbs of salt per gallon  enters and leaves a tank at a rate of 8 gallons/hour.  Suppose  the tank originally contains 7 lbs of salt in 500 gallons of water.  State the initial value problem describing the amount of salt in the tank at time $t$.  Do NOT solve.



Differential equation:  $\underline{\hskip 3in}$ 

Initial Value:  $\underline{\hskip 3in}$ 
\end{document}



[10]~ 2.)  Solve $sin(t) y' + y cos(t) = 5$ 
 \hfil \break(hint:  this is a short problem if you are observant).

$sin(t) y' + y cos(t) = 5$

 $(sin(t) y)'  = 5$  
 
  $\int (sin(t) y)' dt  = \int 5 dt$  

 $\sin(t) y = 5t + C$  

 $ y  = {5t + C \over sin(t)}$  




Answer:$\underline{~~ y  = {5t + C \over sin(t)}~~}$
\end 
