1. MAT 150 Algebra Class #17

2. Objectives Graph and apply exponential functions
Find horizontal asymptotes
Graph and apply exponential growth functions
Graph and apply exponential decay functions
Compare transformations of graphs of exponential functions

3. Exponential Function
If b is a positive real number, b  1, then the function f(x) = bx is an exponential function. The constant b is called the base of the function, and the variable x is the
exponent.

5. Example
Explain how the graph of each of the following functions compares with the graph of y = 2x, and graph each function on the same axes as y = 2x. a. Solution

6. Example
Explain how the graph of each of the following functions compares with the graph of y = 2x, and graph each function on the same axes as y = 2x. b. Solution

7. Example
Explain how the graph of each of the following functions compares with the graph of y = 2x, and graph each function on the same axes as y = 2x. c. Solution

9. Example
Suppose that inflation is predicted to average 4% per year for each year from 2012 to This means that an item that costs $10,000 one year will cost $10,000(1.04) the next year and $10,000(1.04)(1.04) = 10,000(1.042) the following year. a. Write the function that gives the cost of a $10,000 item t years after Solution

10. Example
Suppose that inflation is predicted to average 4% per year for each year from 2012 to This means that an item that costs $10,000 one year will cost $10,000(1.04) the next year and $10,000(1.04)(1.04) = 10,000(1.042) the following year. b. Graph the growth model found in part (a) for t = 0 to t = 13. Solution

11. Example
Suppose that inflation is predicted to average 4% per year for each year from 2012 to This means that an item that costs $10,000 one year will cost $10,000(1.04) the next year and $10,000(1.04)(1.04) = 10,000(1.042) the following year. c. If an item costs $10,000 in 2012, use the model to predict its cost in Solution

13. Example
It pays to advertise, and it is frequently true that weekly sales will drop rapidly for many products after an advertising campaign ends. This decline in sales is called sales decay. Suppose that the decay in the sales of a product is given by S = 1000(20.5x ) dollars where x is the number of weeks after the end of a sales campaign. Use this function to answer the following. a. What is the level of sales when the advertising campaign ends? b. What is the level of sales 1 week after the end of the campaign? c. Use a graph of the function to estimate the week in which sales equal $500. d. According to this model, will sales ever fall to zero?

14. Example
a. What is the level of sales when the advertising campaign ends? b. What is the level of sales 1 week after the end of the campaign? Solution

15. Example
c. Use a graph of the function to estimate the week in which sales equal $500. Solution

16. Example
d. According to this model, will sales ever fall to zero? Solution

17. The Number e
The number e is an irrational number with a decimal approximation of

18. Example
If $10,000 is invested for 15 years at 12% compounded continuously, what is the future value of the investment? Solution

19. Assignment
Pg #1-3 #13-18 #23-25*(Graph both functions on the same graph and then compare the two. You need to be detailed when graphing.) #29,33,40