Suppose the population of mosquitos in a certain area increases at a rate proportional to the current population... in the absense of other factors, the population doubles each week. There are 200,000 mosquitos in the area initially, and predators (birds, etc) eat 20,000 mosquitos /day. Determine the populatoin of mosquitos in the area at any time t.(adsbygoogle = window.adsbygoogle || []).push({});

So I know that for this proportional rate--- we can set up a differential equation of :

dP/dt = rP - (The number eaten)

so dP/dt = 1*P - 140000

I use r =1 due to the fact that the population is doubling--- so increasing by 100 percent, and i am using 140000 because thats how many mosquitos are eaten in a week--- I am trying to get everything so t is in weeks.

So simplified

[tex]dP/dt = P-140000[/tex]

and I simply solve for P using seperable equations, however the book gives the answer as

P = 201977.31 - 1977.31(e^(ln2)t) for 0 < t < 6.6745 (in weeks)

I obviously did not get this solution from the one above--- for what should I be looking to solve this properly and get a consistent answer?

Thanks for your helP!!

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# Having difficulty setting up a Diff Eq for this situation

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