A biologist models the size of an algal population in a laboratory flask by P(t)=…
MATHEMATICS · Multi-part · AP · Calculus BC · Differential Equations · Differential Equations
Problem
A biologist models the size of an algal population in a laboratory flask by
P(t)=1+4e−0.3t1600,
where P(t) is the number of cells and t is measured in hours.
(a) Identify the carrying capacity for this population and determine the initial population size.
(b) Compute t→∞limP(t) and interpret the result in the context of the population.
(c) Describe, in words, how the expression for the instantaneous growth rate dtdP explains why the population’s growth rate is greatest when the population reaches one–half of the carrying capacity.
(d) Explain why the growth rate approaches zero as t→∞, even though the population size approaches a finite limit.