Modeling with first order equations

Story problem time!

The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absense of other factors, the population doubles each week. There are 200,000 mosquitoes in the area initially, and predators (birds, bats and so forth) eats 20,000 mosquitoes/day. Determine the population of mosquitoes in the area at any time.

Thanks for any and all help!

Quote:

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Originally Posted by Proof_of_life

Story problem time!

The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absense of other factors, the population doubles each week. There are 200,000 mosquitoes in the area initially, and predators (birds, bats and so forth) eats 20,000 mosquitoes/day. Determine the population of mosquitoes in the area at any time.

Thanks for any and all help!

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Measure time in days.

$\displaystyle \frac{dM}{dt} = k M - 20,000$ subject to the boundary condition M(0) = 200,000.

You should think about how to use ".... in the absense of other factors, the population doubles each week." to get the value of k .....