1. MAT150 Unit 4-: Exponential Functions Copyright ©2013 Pearson Education, Inc.

2. Objectives  Graph and apply exponential functions  Find horizontal asymptotes  Graph and apply exponential growth/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) = b x is an exponential function. The constant b is called the base of the function, and the variable x is the exponent.

9. Example Suppose that inflation is predicted to average 4% per year for each year from 2012 to 2025. 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(1.04 2 ) the following year. a.Write the function that gives the cost of a $10,000 item t years after 2012. b.Graph the growth model found in part (a) for t = 0 to t = 13. c.If an item costs $10,000 in 2012, use the model to predict its cost in 2025.

11. 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?

13. The Number e The number e is an irrational number with a decimal approximation of 2.718281828.

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