Question

Biologists have proposed a cubic polynomial to model the length l of alaskan rockfish at age a:l = 0.0155a3 − 0.372a2 + 3.95a + 1.21, where l is measured in inches and a is in years. (a) (2 pts) calculate dl da a=12 (b) (2 pts) interpret your answer.

Answer 1

(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.