Chapter 2.5, Problem 3P

(a) Solve the Gompertz equation $dy/dt=ry\ln (K/y),$ subject to the initial condition $y(0)=y_0$.

Hint: You may wish to let $u=ln\left(y/K\right)$.

(b) For the data given in Example $2$ in the text ( $r=0.71$ per year, $K=80.5\times 106$ $kg$, $K=80.5\times {10}^6$, $y_0/K=0.25$), use the Gompertz model to find the predicted value of $y\left(2\right)$.

(c) For the same data as in part $\left(b\right)$, use the Gompertz model to find the time $\tau$ at which $y(\tau )=0.75K$.