Question

A population grows exponentially according to the differential equation dP, dt equals k times P, where P is the population, t is time, and k is a positive constant. If P(0) = A, what is the time for the population to triple its initial value?

Answer 1

https://i.gyazo.com/fd663d2f559c2705695dbfe4c3859b90.png

Answer 2

set \[e^{kt}=3\] solve for \(t\)

Answer 3

hope it is clear that the A is not important
when it triples, it will be 3A and the first step in solving \[3A=Ae^{kt}\] is to divide both sides by \(A\)

Answer 4

\[\ln3/k\]

Answer 5

yes

Answer 6

So it's B?

Answer 7

Yessir, I just tried my hand at it and that is indeed what I got