1. Mice in the House
Charles Pate
Worthing High School
Teacher Tech 2001

2. In the beginning there were six…

3. Six mice invade a house. The population of the mice grows at a rate that is directly proportional to the number of mice present. After two weeks there are now 16 mice living in the house. At the end of the third week, the family cat catches one of the mice.

4. But how many mice were living in the house before the family cat caught one?

5. This problem can be solved by modeling the population growth rate of the mice with a differential equation, solving the differential equation and using the resulting equation along with a set of initial conditions to find out how many mice were living in the house after 3 weeks.
Conclusion

6. A Closer Look at Differential Equations and Population
Growth
A population that grows at a rate that is directly proportional to the number of members present in the population can be modeled by a differential equation. A differential equation is an equation that expresses or contains the rate of change of a function. The rate of change of a function tells how the difference of the dependent variable changes in relation to a change in the difference of the independent variable. A differential equation that expresses the rate of change of a population’s growth as being directly proportion to the number present a t a given time has the following form: