Question

The length of some fish are modeled by a von Bertalanffy growth function. For Pacific halibut, this function has the form L(t) = 200(1 – 0.956e–0.18t ) where L(t) is the length (in centimeters) of a fish t years old.

(a) Find the rate of change of the length as a function of time

Answer 1

Answer:

Rate of change of length as a function of time is given by $\frac{dL(t)}{dt}=34.416e^{-0.18t}$

Explanation:

The length as function of time is given by$L(t)=200(1-0.956e^{-0.18t})$

Differentiating with respect to time we get

$\frac{dL(t)}{dt}=\frac{d(200(1-0.956e^{-0.18t}))}{dt}\\\\\frac{dL(t)}{dt}=200\frac{d(1-0.956e^{-0.18t})}{dt}\\\\=200\times 0.18\times 0.956e^{-0.18t}\\\\\frac{dL(t)}{dt}=34.416e^{-0.18t}$