Question

Von Bertalanffy's equation states that the rate of growth in length of an individual fish is proportional to the difference between the current length L and the asymptotic length LT (in cm). (a) Write a differential equation that expresses this idea. (Let k be the proportionality constant.)

Answer 1

Answer:

dT/dt = k(L-Lt)

Step-by-step explanation:

Let the rate of growth in length be dL/dt

The difference between the current length L and the asymptotic length Lt will be expressed as L-Lt

If the rate of growth in length of an individual fish is proportional to the difference between the current length L and the asymptotic length Lt, this is expressed as;

dT/dt ∝ L-Lt

dT/dt = k(L-Lt) where

k is the proportionality constant

Hence the differential equation that expresses this idea is written as;

dT/dt = k(L-Lt)