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

Rate of change of length as a function of time is given by
`(dL(t))/(dt)=34.416e^(-0.18t)`

Step-by-step 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

`(dL(t))/(dt)=(d(200(1-0.956e^(-0.18t))))/(dt)\\\\(dL(t))/(dt)=200(d(1-0.956e^(-0.18t)))/(dt)\\\\=200* 0.18* 0.956e^(-0.18t)\\\\(dL(t))/(dt)=34.416e^(-0.18t)`