A population of rodents in a wildlife reserve is modeled by the differential equation
MATHEMATICS · Multi-part · AP · Calculus BC · Differential Equations · Differential Equations
Problem
A population of rodents in a wildlife reserve is modeled by the differential equation dtdy=0.02y(1500−y), where t is measured in months and y(t) is the number of rodents.
(1) Determine the population size that yields the greatest instantaneous growth rate.
(2) Calculate that maximum growth rate in rodents per month.
(3) Interpret the meaning of your results in the context of wildlife management for the reserve.