A population p in a restricted environment may grow with

Question

Question: A population, P, in a restricted environment may grow with time, t, according to the logistic function

P =      L      
     1 + Ce^-kt

where L is called the carrying capacity and L, C and k are positive constants.

(a) Find

lim_t→∞ P

Explain why L is called the carrying capacity.

(b) Using a computer algebra system, show that the graph of P has an inflection point at P = L/2.