A wildlife biologist observes that a deer population on a small island grew rapidly…
MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations
Problem
A wildlife biologist observes that a deer population on a small island grew rapidly at first but has recently begun to slow as vegetation is consumed. Which of the following best explains why a logistic, rather than an exponential, model is appropriate for describing the population?
(a) The growth rate is proportional only to the current population size.
(b) The rate of change is proportional to both the current population and the remaining resources, so growth slows as resources are depleted.
(c) The growth rate is proportional only to the remaining resources, becoming zero when the resources are exhausted.
(d) Limited resources impose an upper bound that itself declines over time, so the population will eventually shrink; a logistic model accounts for this decreasing carrying capacity.