Growth in length of haddock: A study by Riatt showed that the maximum length a haddock could be expected to grow is about 53 centimeters. Let D = D(t) denote the difference between 53 centimeters and...

Growth in length of haddock: A study by Riatt showed that the maximum length a haddock could be expected to grow is about 53 centimeters. Let D = D(t) denote the difference between 53 centimeters and the length at age t years. The table below gives experimentally collected values for D.

a. Find an exponential model of D as a function of t.

b. Let L = L(t) denote the length in centimeters of a haddock at age t years. Find a model for L as a function of t.

c. Plot the graph of the experimentally gathered data for the length L at ages 2, 5, 7, 13, and 19 years along with the graph of the model you made for L. Does this graph show that the 5- year-old haddock is a bit shorter or a bit longer than would be expected?

d. A fisherman has caught a haddock that measures 41 centimeters. What is the approximate age of the haddock?