Exponential Growth and Decay
MAT 135: Calculus
Rate of population growth
is proportional to 
size of population at any time
P(t)
P'(t) or dP/dt
Differential equation
Solution to a differential equation = A function satisfying the equation
Suppose the population of small town is 20,000 people in 1950 and grows at a rate of 5% per year. Assuming unlimited growth: 
Set up a differential equation modeling the growth rate. 
Find the solution for the differential equation. 
Use the solution to predict the population in 2010. 
Newton's Law of Cooling: The rate at which a hot object cools off is proportional to the difference between the object's temperature and the temperature of the surrounding space. 
This pizza came out of the oven at a temperature of 400 degrees. The kitchen is at a temperature of 75 degrees. After half an hour, the pizza has cooled to 150 degrees. 
What is the temperature of the pizza after another half hour? 
How long does it take the pizza to cool to 90 degrees?