A skull cleaning factory cleans animal skulls of deer buffal

A skull cleaning factory cleans animal skulls of deer, buffalo and other types of animals using flesh-eating beetles. The factory owner started with only 6 adult beetles. After 25 days, the beetle population grew to 18 adult beetles. How long did it take before the beetle population was 6 comma 000 beetles?

Solution

The population tripples in 25 days.
The population after t days is
P(t) = P·3^(t/25)

Solve for t:
6000 = 6·3^(t/25)
on dividing by 6 both sides we get:
1000 = 3^(t/25)
log(1000)/log3 = t/25
multiply both sides by 25 we get:
t = 25log(1000)/log3 157 days