• Support PF! Buy your school textbooks, materials and every day products Here!

Differential Equations and population

  • #1

Homework Statement



Consider a population p of field mice that grows at a rate proportional to the current population, so that dp/dt=rp.

Find the rate constant r if the population doubles in 30 days.

Find r if the population doubles in N days.

Homework Equations



...


The Attempt at a Solution



This is the first time I've seen differential equations, and I have no idea how to do this problem, which appears to be relatively easy. If the population doubles in 30 days, then the rate of change of the population is 2P(0)/30, right? So does this mean I have to solve for P(t)--we haven't really even talked about solving anything yet.
 

Answers and Replies

  • #2
Char. Limit
Gold Member
1,204
14
Well, this is fortunately a pretty easy differential equation to solve. Just multiply both sides by dt and then divide both sides by p. You should be able to integrate both sides then.
 
  • #3
Gotcha. Thanks.
 

Related Threads on Differential Equations and population

Replies
4
Views
3K
Replies
1
Views
3K
Replies
1
Views
952
Replies
2
Views
2K
Replies
5
Views
3K
Replies
0
Views
3K
Replies
9
Views
14K
Replies
5
Views
2K
Replies
5
Views
820
  • Last Post
Replies
1
Views
1K
Top