A modification to the logistic equation which accounts for the influence of the resources available on the growth of the population results in the equation:
where , and are positive constants. Determine the solution of this equation, given that when . Show that the population size tends to the carrying capacity of the environment as increases.
Source: R.L. Rosenberg. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 45: Question 4, p. 134)