(a) To answer this item, we are to differentiate the given equation, l, in terms of a. This is as shown below.
dl/da = 3(0.0155)a² - 2(0.372)a + 3.95
Substituting the known value, a = 12
dl/da = (3)(0.0155)(12)² - 2(0.372)(12) + 3.95
Simplify,
dl/da = 1.718
(b) The answer in a tells us that the length of the alaskan rockfish will change at a rate of 1.718 inches/year when it is already 12 years old.
