A wildlife reserve monitors the instantaneous population growth rate of a certain…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A wildlife reserve monitors the instantaneous population growth rate of a certain fish species. The growth rate, in fish per year, is modeled by
g(t)=200e−0.02t−50,0≤t≤10,
where t is the number of years since a conservation program began.
(a) Find the exact net change in the fish population during the first 10 years of the program.
(b) Determine the average population growth rate over this 10-year interval and include proper units.
(c) Solve for the time t=c in [0,10] at which the instantaneous growth rate equals the average growth rate found in part (b). Give your answer to three decimal places.
(d) Interpret the significance of the value of c in the context of the fish population.