Differential Equations Problem, logistic models

  • Thread starter beccajd
  • Start date
  • #1
2
0

Homework Statement



Given that a population, P, after t months, can be modeled by the logistic model
dP/dt = .3 P (3.5 - P/40).
P(0) = 30

a) Solve the diff eq

b) Find the population after 2.5 months

c) Find lim P(t) as t -> infinity

Homework Equations



P(t) = P0 P1 /(P0 + (P1 - P0 )e^(-AP1 t))

A = k3 /2
P1 = (2k1 / k3 ) +1

The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
BruceW
Homework Helper
3,611
121
hi, beccajd
You have pretty much done part a) already. You have written down the correct solution. So now you can work out what k1 and k3 should be, by looking at the numbers in the equation given to you. I think this is everything they expect from part a). Try doing part b), it shouldn't be too difficult, since you have got the equation for it.
 

Related Threads on Differential Equations Problem, logistic models

Replies
3
Views
5K
Replies
1
Views
4K
Replies
5
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
900
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
704
Replies
9
Views
15K
  • Last Post
Replies
0
Views
1K
Top