(a) solve the gompertz equation
dy/dt = ry ln(k/y),
subject to the initial condition y(0) = y0. hint: you may wish to let u = ln(y/k).
(b) for the data given in example 1 in the text (r = 0.71 per year, k = 80.5 × 106 kg, y0/k = 0.25), use the gompertz model to find the predicted value of y(2).
(c) for the same data as in part (b), use the gompertz model to find the time τ at which y(τ) = 0.75k.