1. 1.3 Exponential Functions

2. Interest If $100 is invested for 4 years at 5.5% interest compounded annually, find the ending amount. This is an example of an exponential function: f(x) = k●a x

3. Graph for in a [-5,5] by [-2,5] window: Where is ?

4. Population growth can often be modeled with an exponential function: Ratio: World Population: 1986 4936 million 1987 5023 1988 5111 1989 5201 1990 5329 1991 5422 The world population in any year is about 1.018 times the previous year. in 2010: About 7.6 billion people. Nineteen years past 1991.

5. Radioactive decay can also be modeled with an exponential function: Suppose you start with 5 grams of a radioactive substance that has a half-life of 20 days. When will there be only one gram left? After 20 days: 40 days: t days: In Pre-Calc and in AB Cal you solved this using logs. Today we are going to solve it graphically for practice.

6. Many real-life phenomena can be modeled by an exponential function with base, where. e can be approximated by: Graph: y=(1+1/x)^x in a [-10,10] by [-5,10] window. Use “trace” to investigate the function.

7. y = e x and y = e –x are used as forms of exponential growth and decay. Interest Compounded Continuosly: y = Pe rt P is the principle investment r is the interest rate (decimal) t is the time (years)