Answer
(a)$D(t)=\frac{ 29.25e^{0.03572t} }{ 0.03572 }-118.87 $
(b)$D(35)=2739.84$
Work Step by Step
$D^{'}(t)=29.25e^{0.03572t}$
(a)
$D'{t}=\frac{d( D)}{dt}=29.25e^{0.03572t}$
$\frac{d( D)}{dt}=29.25e^{0.03572t}$
$d(D)=29.25e^{0.03572t} dt$
Taking antiderivative
$D(t)=\frac{ 29.25e^{0.03572t} }{ 0.03572 }+C$
Putting $D(0)=700$
$700=\frac{ 29.25 }{ 0.03572 }+C$
$C=-118.87$
$D(t)=\frac{ 29.25e^{0.03572t} }{ 0.03572 }-118.87 $
(b)
Putting $t=35$
$D(35)=\frac{ 29.25e^{0.03572\times 35} }{ 0.03572 }-118.87 =2739.84$
