A population of mice, initially numbering 30, is kept in conditions that can support a population size of 120. The rate of increase in the population of size is assumed to be given by the equation , where and are positive constants. Find the formula giving the number of mice months later, if, after one month, the population numbers 80.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 44: Question 5, p. 132)