Consider the differential equation

$\frac{dP}{dt}=k{P}^{1+c},$

$[0,),$ that $is,P(t)ast.$ See Example $1in$ that section.

$(a)$ Suppose for $c=0\mathrm{.}01$ that the nonlinear differential equation

$\frac{dP}{dt}=k{P}^{1\mathrm{.}01},k>0,tto$ six decimal places.$P(t)=(0\mathrm{.}977237-0\mathrm{.}002825t{)}^{-100}$

$t{T}^{-}.$ Find $T.(Round$ your answer $to$ the nearest month.$)$

$T=$

months

$(c)$ From part $(a),$ what $isP(40)?P(80)?(Round$ your answers $to$ the nearest whole number.$)$

$P(40)=$

$P(80)=908$