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 14 adult beetles. After 37 days, the beetle population grew to 42 adult beetles. How long did it take before the beetle population was 14 comma 000 beetles?

After 37 days, the population is three times,

That is,

N37 = 42/14 = 3

Therefore, the relationship between initial population and population after t days, is given as;

N = No*3^ (t/37)

Where, N = Population after t days, No = Initial population = 14 beetles, t = number of days.

Therefore,

14,000 = 14*3^ (t/37)

1000 = 3^ (t/37)

Taking natural logs on both sides,

log 1000 = (t/37) log 3

3 = (t/37) * 0.4771

6.2877 = t/37

t = 37*6.2877 = 232.645 days ≈ 233 days