logistic growth models

I'm having troubles figuring out how to set up the formula before integration for differential equations. Here's the problem:

"The population of mosquitoes in a certain area increases at a rate proportional to the current population, an in the absence of other factors, the population doubles each week. There are 200,000 mosquitoes in the area initially, and predators eat 20,000 mosquitoes a day. Determine the population of mosquitoes at any time. "


Any help will be greatly appreciated.

If we indicate with y the mosquitoes as function of time, the 'growth model' is expressed by the equation...



... where a is the 'growth rate' in absence of other factors and k is the 'killing rate' due to predators...

Kind regards