# Transcribed Image Text: (2) A common growth model for a population P(t) is so-called logistic growth: dP — k. Р. (М-

Excerpt |
---|

that for large times, the general solution (3) yields lim;→∞ P(t) = M (c) Now solve a special case of the logistic equation with k = 3, M = 2 and Po = 1. Use separation by variables and for the P-integral use partial fractions. |

Transcribed Image Text: (2) A common growth model for a population P(t) is so-called logistic growth:

dP

— k. Р. (М- Р)

dt

(2)

For small times the growth dP/dtwill be roughly proportional to P, but for later times, the growth will

slow down because M – P will approach zero. In the logistic equation the constant k is called the growth

factor and M is called the carrying capacity. Ts differential equation can be solved as

M

P(t)

(3)

(* -1)

M

1+

Ро

kMt

e

where P(0) = Po-

(a) Show that when we insert t = 0 in the general solution (3), we indeed find P(0) = Po.

(b) Show that for large times, the general solution (3) yields lim;→∞ P(t) = M

(c) Now solve a special case of the logistic equation with k = 3, M = 2 and Po = 1. Use separation by

variables and for the P-integral use partial fractions.

### Need your ASSIGNMENT done? Use our paper writing service to score better and meet your deadline.

Click Here to Make an Order Click Here to Hire a Writer