Law of uninhibited growth

Following the Law of Uninhibited Growth, if there are initially 1000 mosquitoes in a colony and 1900 mosquitoes after 1 day.

What is the size of the colony after 4 days?

And about how many days until the colony reaches 40,000?

M(t) = M(0) x e^kt......where M(t) is the number at time t and M(0) is the starting amount.

=> 1900 = 1000 x e^k

=> e^k = 1.9

i.e. k = ln1.9 = 0.642

so, M(t) = 1000 x e^0.642t

then, if the population is 40,000 we have:

40000 = 1000 x e^0.642t

=> e^0.642t = 40

i.e. 0.642t = ln40

=> t = 5.7 days

:)>