Question

N(t)=2400000e^0.03t

What time is required for the population to tripple if N is the population size at time while t is the number of years

Answer 1

$N=2400000e^{0.03t_1} \;\;\;(1) \\ 3N = 2400000e^{0.03t_2} \;\;\;(2)$

$(t_2 -t_1)$ is time required for the population to tripple

Divide (2) by (1):

$\frac{3N}{N} = \frac{2400000e^{0.03t_2}}{2400000e^{0.03t_1}} \\ 3 = \frac{e^{0.03t_2}}{e^{0.03t_1}} \\ 3 = e^{0.03(t_2-t_1)} \\ ln(3) = 0.03(t_2-t_1) \\ (t_2-t_1) = \frac{ln(3)}{0.03} = \frac{1.098}{0.03} = 36.6 \; years$

Answer: 36.6 years