Question

A population grows exponentially according to the differential equation dP/dt = kP, 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

@hartnn

Answer 2

dP/dt = kP
This can be solved by variable separation method.

(1/P) dP = k dt
and Integrate both sides.

We will have a constant of Integration, say C, that can be found using the initial Condition,
P(0) = A

which means plug in t=0, P =A, to get the value of C.

Lastly, we need when the population triples its initial value,
so we need when P becomes 3A.

Just plug in P=3A to get 't' which will be your answer :)