Question

Denote L(t) as the length of a fish at time t, and assume that the fish grows according to von Bertalanffy's equation: dL/dt = k(24 - L(t)) with L(0) = 6.

Answer 1

The von Bertalanffy's equation for the growth of a fish can be solved by separating variables and integrating both sides. The specific solution can be found using the initial condition.

Step-by-step explanation:

The von Bertalanffy's equation for the growth of a fish is given by dL/dt = k(24 - L(t)). To solve this differential equation, we can separate variables and integrate both sides.

Starting with dL = k(24 - L(t))dt, we can rearrange and divide both sides by (24 - L(t)) to get 1/(24 - L(t)) dL = kdt.

Integrating both sides gives us the equation ln|24 - L(t)| = kt + C, where C is the constant of integration. Using the initial condition L(0) = 6, we can solve for C and find the specific solution.