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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:  $\underline{~~y' = ry~~}$ 

Initial Value:  $\underline{~~y(0) = 75~~}$ 

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


D.)  $y = Ce^{rt}$ \hfill 

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


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:  $\underline{~~Q' = 24 - {8Q \over 500}~~ or~~ Q' = 24 - {2Q \over 125}}$ 

Initial Value:  $\underline{~~Q(0) = 7~~}$ 



Let $Q(t) =$ amount of salt (in pounds) in the tanke at time $t$.

${dQ \over dt} =$ Rate in - rate out $= ({3lbs \over 1 gallon})({8 gallons \over 1 hour}) -  ({Q(t)lbs \over 500 gallon})({8 gallons \over 1 hour})$


$Q' = 24 - {8Q \over 500} =  24 - {4Q \over 250} = 24 - {2Q \over 125}$

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