Consider the differential equation

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

infinite time interval $[0,),$ 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.$P(t)=(0\mathrm{.}9772-0\mathrm{.}000957t{)}^{-100}$

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

$T=1022$months

$(c)$ From part $(a),$ what $isP(70)?P(140)?(Round$ your answers $to$ the nearest whole number.$)$

$P(70)=$

$P(140)=25500000$