Growth in length: In the fishery sciences it is important to determine the length of a fish as a function of its age. One common approach, the von Bertalanffy model, uses a decreasing exponential...

Growth in length: In the fishery sciences it is important to determine the length of a fish as a function of its age. One common approach, the von Bertalanffy model, uses a decreasing exponential function of age to describe the growth in length yet to be attained; in other words, the difference between the maximum length and the current length is supposed to decay exponentially with age. The following table shows the length L, in inches, at age t, in years, of the North Sea sole.

The maximum length attained by the sole is 14.8 inches.

a. Make a table showing, for each age, the difference D between the maximum length and the actual length L of the sole.

b. Find the exponential function that approximates D using the logarithm as a link.

c. Find a formula expressing the length L of a sole as a function of its age t.

d. Draw a graph of L against t.