I have been having some trouble understanding how to solve this question.

Question

Given that a colony of ants in an experiment follows the law of uninhibited growth for

the first 7 months. The colony has tripled in population after 6 months, how many months

did it take for the colony to double its initial population?

Answer 1

This is a continuous growth problem So use the formula y= A e^kt where y is final value a is initial value k is growth factor a t is time

First we have to solve for k

If the population triples in 6 months then y/a =3 and t= 6

3= e^6k

ln3 =ln e^6k

ln 3 = 6k k = (ln3)/6 k=.1831 We can use this now to get time it takes to double. In this case y/a=2

2= e^.1831t

ln 2 = ln e^.1831t

ln 2 = .1831 t t= (ln2)/.1831 t= 3.7856 months