# Math Help - A problem on ODE modeling

1. ## A problem on ODE modeling

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

It seems to be simple but i still cannot figure out the equation for this question.

The solution is dp/dt=(In2)*P-140000.

The '140000' indicates the equation actually measures in weeks so it is 20,000*7=140000.

Then how about the 'In2' ? it says without any external factors the population doubles each week then where does this "In2" come? why not just "2"...

thank you so much for you valuable help.

2. Originally Posted by rexhegemony

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

It seems to be simple but i still cannot figure out the equation for this question.

The solution is dp/dt=(In2)*P-140000.

The '140000' indicates the equation actually measures in weeks so it is 20,000*7=140000.

Then how about the 'In2' ? it says without any external factors the population doubles each week then where does this "In2" come? why not just "2"...

thank you so much for you valuable help.

Without predation the population satisfies:

$\frac{dP}{dt}=kP$

which has solution $P(t)=P_0 e^{kt}$, as the population doubles in 1 week we have from this:

$e^k=2$

or:

$k=\ln(2)$

CB

3. oh very clear!
thank you so much!