The question:

For this exercise, round all regression parameters to three decimal places.

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.

t = age L = Length 1 |3.7 2 |7.5 3 |10 4 |11.5 5 |12.7 6 |13.5 7 |14 8 |14.4
Suppose the maximum length attained by the sole is

15.0 inches.

(a) Make a table showing, for each age, the difference

*D* between the maximum length and the actual length

*L* of the sole.

t = age D = Difference 1 |11.3 2 | 7.5 3 | 5 4 | 3.5 5 | 2.3 6 | 1.5 7 | 1 8 |0.6
(I was only able to get row 8 by using the information underneath the previous table.)

Why?
(b) Find the exponential function that approximates

*D*. (Round all regression parameters to three decimal places.)

*D* =

17.466(.662)^t
(c) Find a formula expressing the length

*L* of a sole as a function of its age

*t*. (Round all parameters to three decimal places.)

*L* =

a + b ln (t) L = 3.939 + 5.261 ln (t)
(I thought this would be

, but that was incorrect.)