A model for a certain population P(t) is given by the initial value problem

dP

dt

= P(10³ 10⁷P), P(0) = 100, where t is measured in months.

At what time (i.e., after how many months) will the populaton be equal to one third of the limiting value in (a)? (Do not round any numbers for this part. You work should be all symbolic.)