Concept explainers
(a) Show that if P satisfies the logistic equation (4), then
(b) Deduce that a population grows fastest when it reaches half its carrying capacity.
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Chapter 9 Solutions
Calculus, Early Transcendentals
- Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .arrow_forwardWhat is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?arrow_forward
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