Question

The population of a bee hive is growing with a monthly percentage rate compounded continuously. The population doubles in 3 months.
Find the monthly percentage rate according to the exponential growth function. Leave your answer in terms of ln.

Answer 1

Answer:

$r = \frac{\ln{2}}{3}$

Step-by-step explanation:

The exponential growth function is:

$P(t) = P(0)e^{rt}$

In which P(t) is the population after t months, P(0) is the initial population and r is the monthly percentage rate.

The population doubles in 3 months.

This means that $P(3) = 2P(0)$

We use this to find r.

$P(t) = P(0)e^{rt}$

$2P(0) = P(0)e^{3r}$

$e^{3r} = 2$

$\ln{e^{3r}} = \ln{2}$

$3r = \ln{2}$

$r = \frac{\ln{2}}{3}$