Differential Equations and population

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SUMMARY

The discussion focuses on solving a differential equation related to population growth of field mice, modeled by the equation dp/dt = rp. The key task is to determine the rate constant r when the population doubles in 30 days. The solution involves integrating the equation after rearranging it, leading to the conclusion that the population growth can be expressed in terms of the initial population and the rate constant.

PREREQUISITES
  • Understanding of differential equations, specifically first-order linear equations.
  • Familiarity with integration techniques in calculus.
  • Knowledge of exponential growth models in population dynamics.
  • Basic algebra for manipulating equations.
NEXT STEPS
  • Study the method of separation of variables in differential equations.
  • Learn about exponential growth and decay models in population studies.
  • Explore the concept of rate constants in biological systems.
  • Practice solving differential equations using real-world applications.
USEFUL FOR

Students studying calculus, particularly those interested in applications of differential equations in biology, as well as educators looking for examples of population modeling.

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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.
 
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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.
 
Gotcha. Thanks.
 

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