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 400,000 mosquitoes in the area initially, and predators (birds, bats, and so forth) eat 40,000 mosquitoes/day. Determine the population of mosquitoes in the area at any time. (Note that the variable t represents days.) Enter an exact answer.
The initial number of mosquitoes is 400000, and they double each day. This represents an exponential growth equation. If t represent days and P represent the population of the mosquitoes, hence this can be represented by the equation:
Also, the predators eat the mosquitoes at a rate of 40,000 mosquitoes/day. This means that each day, the mosquitoes reduce by 40000t, therefore this can be represented by:
