1. 1.5 Exponential Functions Math 150 Introduction to Calculus

2. An Exponential Function  As an example to begin with, consider the function f(t) = 2 t. Then f(1) = 2, f(2) = 2 2 = 4 and so on.  The number 2 is called the base of the function, and its exponent is variable.  Exponential functions show up in a variety of applications.

3. Population Growth  Population growth is one example  The rate of growth depends on the size of the population

4. Drug Concentrations  The amount of a drug in the bloodstream decreases naturally due to metabolic activity  Over time, the amount leaving the blood stream depends on the amount in the bloodstream

5. Exponential Functions

6. Linear vs. Exponential

7. Seeing Patterns in Data

8. …and the Solution

9. The number e  Yes, e is a number. It is a constant value like   e is a commonly used base for exponential functions, f(t) = e t  e is special because the function f(t) = e t has a rate of change that makes it useful in finance, science and mathematics

10. Families of Exponentials  In the graphs below, functions for exponential growth and exponential decay are plotted for different values of the base a  The graph of f(t) = e t is shown on the left