1. Essential Skills: Graph Exponential Functions Identify behavior that displays exponential functions

2.  An exponential function is a function that can be described by an equation in the form y = ab x  Conditions: a ≠ 0, b ≠ 1, and b > 0  Examples: ▪ y = 2(3) x ▪ y = 4 x ▪ y = (½) x

3.  Example 1: Graph y = 4 x. Find the y-intercept and state the domain and range  Make a table of x-values (your choice) and fill in the chart. ▪ Advice ▪ Always choose x = 0 (the y-int) ▪ Choose at least one positive and one negative number x4x4x y 4 -1 ¼ 04040 1 14141 4 24242 16

4.  Example 1: Graph y = 4 x. Find the y-intercept and state the domain and range  Plot each point from your table  Connect your points with a smooth line  The domain (x-values) are all real numbers  The range (y-values) are all positive real numbers x4x4x y 4 -1 ¼ 04040 1 14141 4 24242 16

5.  Example 1: y = 4 x  Estimate the value of 4 1.5  Calculator: 4^(1.5) = 8

6.  Graphing Exponential Growth  Example: Graph y = 3 ● 2 x  Step 1: Make a table of values  Step 2: Graph the coordinates with a smooth curve x3 ● 2 x y -23 ● 2 -23 / 4 = 0.75 3 ● 2 -13 / 2 = 1.5 03 ● 2 0 3 13 ● 2 1 6 23 ● 2 2 12

7. EExample 2: y = 5 x EEstimate the value of 5 0.25 AAbout 1.5

8.  Graphing Exponential Growth  Example: Graph y = ¼ x  Step 1: Make a table of values  Step 2: Graph the coordinates with a smooth curve ▪ On board

9. EExample 3: y = ¼ x EEstimate the value of ¼ -1.5 AAbout 8

10.  Assignment  Page 427  1 – 5, 11 – 19 (odds)

11. Essential Skills: Graph Exponential Functions Identify behavior that displays exponential functions

12.  Exponential growth  y = a ● b x  Note that this is the same as any exponential function, except that the base in exponential growth is always greater than 1.  Why? Starting amount (when x = 0) Base (greater than 1) Exponent

13.  Exponential decay  y = a ● b x  Note that this is the same as exponential growth, except the base is between 0 and 1.  Why? Starting amount (when x = 0) Base (between 0 and 1) Exponent

14.  Example 3  Some people say that the value of a new car decreases as soon as it’s driven off the dealer’s lot. The function V = 25,000(0.82) t 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. What is the value of the car after five years?  V = 25000(0.82) t ▪ t = 5 years ▪ V = 25000(0.82) 5 ▪ V ≈ $9268

15. YYour Turn TThe function V = 22,000(0.82) t models the depreciation of the value of a new car that originally cost $22,000. V represents the value of the car and t represents the time in years from the time the car was purchased. What is the value of the car after one year? VV ≈ $18,040

16. EExample 4 DDetermine whether the set of data displays exponential behavior. Explain why or why not. LLook for a pattern ▪T▪The domain increases by regular intervals of 10 ▪L▪Look for a common pattern among the range ▪1▪102562.5156.25 x2.5x2.5x2.5 ▪S▪Since the range values have a common factor, the equation for the data may involve (2.5) x, and the data is probably exponential. x0102030 y102562.5156.25

17. YYour Turn DDetermine whether the set of data displays exponential behavior. Explain why or why not. ▪Y▪Yes, the data is exponential ▪E▪Each range value is being multiplied by 0.5 x0102030 y100502512.5

18.  Assignment  Page 427 ▪ 7 (part b only), 8, 9 ▪ 20 (part a only), 21 - 24