## Differential Equation (Application)

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)

## Differential Equation (Application)

The growth of a cell depends on the flow of nutrients through its surface.  Let be the weight of the cell at time .  Assume that for a limited time the growth rate is proportional to .  (If the density remains constant, then is proportional to , where D is the diameter of the cell, and the surface area is proportional to , or equivalently ).

Hence for some positive constant .  Find the general solution to this differential equation.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 44: Question 4, p. 132)

## Differential Equation

The rate at which weight is lost by an animal suffering from a viral infection is observed to satisfy the relationship for .  Here is the weight loose, as a percentage of the animals original weight, weeks from the time of infection.  Find the function giving the percentage weight loss at time , and determine the percentage weight loss when the animal dies eight weeks later.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 44: Question 3, p. 132)