A pharmaceutical solution in a sealed container has volume in milliliters at time…

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A pharmaceutical solution in a sealed container has volume

V(t)

in milliliters at time

t

hours and satisfies

\dfrac{dV}{dt}=kV

with

V(0)=200

mL. The proportionality constant is

k=0.08\text{ h}^{-1}

. (a) Calculate

\dfrac{dV}{dt}

in milliliters per hour at

t=4

hours. (b) Express the value obtained in part (a) as a percentage of the current volume

V(4)

. (c) At what time

t

(to the nearest tenth of an hour) will the instantaneous rate of change first exceed

20

mL per hour? Show work leading to your answer.