The population of a bee hive is growing with a monthly percentage rate compounded continuously. The population doubles in 3 months.

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

2P = P(e^rt) where t = years

2 = e^rt = e^(r/4)

ln2 = r/4

r = 4ln2 = annual rate of change

or if do t in months then

2 = e^3r

ln2 = 3r

r = (1/3)ln2 = monthly rate of change

Queen Bee has endless male drones to serve Her