The length (in centimeters) of a common commercial fish is approximated by the von-Bertalanffy growth function where a, b, and k are positive constants. Select the graph of f.

Question

The length (in centimeters) of a common commercial fish is approximated by the von-Bertalanffy growth function  where a, b, and k are positive constants. Select the graph of f.

Quizplus · Accepted Answer

The Von-Bertalanffy growth function is mainly used to model the growth of living organisms. It is an S-shaped curve that approaches an asymptotic maximal length. The function can be represented as:
f(t) = L(1 - e^(-k(t-t0))),
where L is the maximum possible length, k is a growth rate constant, and t0 is a time offset.

In this case, the length of a fish is modeled using the same function. Therefore, the correct graph should be an S-shaped curve that approaches an asymptotic maximal length.

Option A represents an S-shaped curve that approaches a maximum length of around 60 cm. Therefore, it is the best choice for this question.

Option B represents a constant function that does not change with time. It does not represent the growth of a fish.

Option C, D, and E represent linear functions with positive slopes that increase with time. They do not represent the growth of a fish.

Therefore, the best choice is A.

The Length (In Centimeters) of a Common Commercial Fish Is