$($a$)$ Solve the Gompertz equation

$\frac{dy}{dt}=ryln(\frac{K}{y})$

subject to the initial condition $y(0)=y_0.$ Hint: You may wish to let $u=ln(\frac{y}{K}).$

$y(t)=$

$$

$($b$)$ For the given data $r=0\mathrm{.}71$ per year, $K=80,300kg,$ and $\frac{y_0}{K}=0\mathrm{.}27.$ Use the Gompertz model to find the predicted value of $y(7).($Round your answer to the nearest integer.$)$

$y(7)=$

$$

$($c$)$ For the same data as in part $($b$),$ use the Gompertz model to find the time $$ at which $y()=0\mathrm{.}79K.($Round your answer to two decimal places.$)$

$=$