MATHEMATICS · Multi-part · AP · Calculus BC · Differential Equations · Differential Equations
Problem
In a forest ecosystem, the growth rate of a beetle population B(t) (in thousands of beetles) is described by the non-standard differential equation
dtdB=225B−0.03B2,
where t is measured in weeks.
(a) Rewrite the differential equation in standard logistic form and determine the numerical values of the two logistic parameters.
(b) State the carrying capacity for the beetle population, including units.
(c) Determine the value of B at which the population is increasing at its maximum rate, and calculate that maximum rate in thousands of beetles per week.