Question

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?

Answer 1

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