From a 2005 study by the Fisheries Research Services in Aberdeen, Scotland, we infer that the average length in centimeters of the species Clupea harengus (Atlantic herring) as a function of age t (in years) can be modeled by the function

for 0 ≤ t ≤ 13. See Figure 1.

(a) How fast is the average length changing at age t = 6 years?
(b) Use a plot of L'(t) to estimate the age t at which average length is changing at a rate of 5 cm/yr.

Transcribed Image Text:

L(t) = 32(1 − (1 + 0.37t+ 0.068t² +0.0085t³ +0.0009¹)-¹) -