A population of fish in a lake is modeled (in thousands) by
P(t)=12(e0.4t−e0.1t),0≤t≤10,
where t is measured in years since the species was introduced.
(a) Compute P′(t) and explain its biological meaning.
(b) Determine all critical points of P in the interval 0<t<10.
(c) Use an appropriate derivative test to decide at which time(s) within 0<t<10 the population attains its maximum size. Justify your answer.
(d) Estimate the maximum population, in actual number of fish, that the lake supports during the first 10 years.