1. 5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find 4.1  (-0.5) Simplify each expression 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) 5.A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green? 6. Which of the following is a true statement Standardized Test Practice: ACBD 8/4 < 4/8-4/8 < -8/4-4/8 > -8/4-4/8 > 4/8

2. Lesson 10-5 Exponential Functions

3. Transparency 5 Click the mouse button or press the Space Bar to display the answers.

4. Transparency 5a

5. Objectives Graph exponential functions Identify data that displays exponential behavior

6. Vocabulary Exponential function –

7. Key Concept xxxx

8. Example 1a Graph the ordered pairs and connect the points with a smooth curve. Answer:The y-intercept is 1. Graph State the y-intercept. 93232 2 33131 1 13030 0 3 –1 –1 y3x3x x

9. Example 1b The graph represents all real values of x and their corresponding values of y for Use the graph to determine the approximate value of Answer:The value of y is about 5 when Use a calculator to confirm this value.

10. Example 2a Graph State the y-intercept. Graph the ordered pairs and connect the points with a smooth curve. Answer:The y-intercept is 1. 1 10 4–1 yx

11. Example 2b Use the graph to determine the approximate value of Answer:The value of y is about 8 when Use a calculator to confirm this value.

12. Example 3 Depreciation People joke that the value of a new car decreases as soon as it is driven off the dealer’s lot. The function models the depreciation of the value of a new car that originally cost $25,000. V represents the value of the car and t represents the time in years from the time the car was purchased. Graph the function. What values of V and t are meaningful in the function. Use a graphing calculator to graph the function. Answer: Only the values of V  25,000 and t  0 are meaningful in the context of the problem.

13. Example 3 cont B. What is the value of the car after one year? Original equation Use a calculator. Answer:After one year, the car’s value is about $20,500. C. What is the value of the car after five years? Original equation Use a calculator. Answer:After five years, the car’s value is about $9270.

14. Example 4a Determine whether the set of data displays exponential behavior. Method 1Look for a Pattern The domain values are at regular intervals of 10. Look for a common factor among the range values. 10 25 62.5 156.25 x 0102030 y 102562.5156.25 Answer:Since the domain values are at regular intervals and the range values have a common factor, the data are probably exponential. The equation for the data may involve (2.5) x.

15. Example 4a cont Answer:The graph shows a rapidly increasing value of y as x increases. This is a characteristic of exponential behavior. Method 2Graph the Data

16. Example 4b Determine whether the set of data displays exponential behavior. Method 1Look for a Pattern The domain values are at regular intervals of 10. The range values have a common difference of 15. 10 25 40 55 +15 x 0102030 y 10254055 Answer:Since the domain values are at regular intervals and there is a common difference of 15, the data display linear behavior.

17. Example 4b cont Answer:The graph is a line, not an exponential function. Method 2Graph the Data

18. Summary & Homework Summary: –An exponential function is a function that can be described by the equation of the form y = a x, where a > 0 and a ≠ 1 Homework: –pg