A zoologist is writing a dissertation on the impact of the fish population in Lake Maben since the Bellmore Company built a factory nearby. Initial sampling shows that the fish population can be modeled byp(t) = 11 · (0.6)t 0 ≤ t ≤ 10 where t represents the number of years since the factory opened, and p(t) represents the fish population in hundreds.(a) Determine p'(t). p'(t) =11·(.6)tln(.6)
(b) Evaluate p'(1).
(Round your answer to two decimal places.)
p'(1) = 3.37
Interpret p'(1).
3 year(s) after the factory opened, the fish population was decreasing at a rate of 3.37 fish per year.
Compare p'(1) to p'(7).
7 years after the factory opened, the fish population was decreasing at a rate of _______fish per year, which is less than the decay rate one year after the factory opened.