Step-by-step explanation:
Continuous exponential growth model:
[tex]population = population(t = 0) \times e ^{ \alpha t} [/tex]
Where α is the growth rate parameter.
So if t is the starting point and t+t1 is the point that population is doubled:
[tex]\frac{population(t + t1)}{population(t)} = \frac{2 \times population(t)}{population(t)} = 2 = {e}^{ \alpha \times t1 } [/tex]
So:
[tex] ln(2) = \alpha \times t1[/tex]
And as a result, t1, the time needed for the population to double at ANY given point is equal to:
[tex] t1 = \frac{ ln(2) }{ \alpha } [/tex]
