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.

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Mathematics

16 October, 10:32

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.

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Bartlett · 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.