Differential Equations and population

[Bogus_Roads]

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

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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.

 

[Char. Limit]

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.

 

[Bogus_Roads]

Gotcha. Thanks.