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(a) Solve the Gompertz equation dy/dt = ry ln(K/y) subject to the initial condition y(0) = y0

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(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.