Essential Skills Graph Exponential Functions Identify behavior that

Essential Skills: Graph Exponential Functions Identify behavior that displays exponential functions 7 -5: Exponential Functions

7 -5: Exponential Functions �An exponential function is a function that can be described by an equation in the form y = abx Conditions: a ≠ 0, b ≠ 1, and b > 0 Examples: ▪ y = 2(3)x ▪ y = 4 x ▪ y = (½)x

7 -5: Exponential Functions �Example 1: Graph y = 4 x. Find the yintercept and state the domain and range Make a table of x-values (your choice) and fill in the chart. x 4 x y ▪ Advice -1 4 -1 ¼ 0 40 1 1 41 4 2 42 16 ▪ Always choose x = 0 (the y-int) ▪ Choose at least one positive and one negative number

7 -5: Exponential Functions � Example 1: Graph y = 4 x. Find the y-intercept and state the domain and range x 4 x y -1 4 -1 ¼ 0 40 1 1 41 4 2 42 16 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

7 -5: Exponential Functions �Example 1: y = 4 x �Estimate the value of 41. 5 Calculator: 4^(1. 5) = 8

7 -5: Exponential Functions �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 x 3 ● 2 x y -2 3 ● 2 -2 -1 3 ● 2 -1 0 3 ● 20 3 1 3 ● 21 6 2 3 ● 22 12 3/ 4 3/ 2 = 0. 75 = 1. 5

7 -5: Exponential Functions �Example 2: y = 5 x �Estimate the value of 50. 25 About 1. 5

7 -5: Exponential Functions �Graphing Exponential Growth Example: Graph y = ¼x Step 1: Make a table of values Step 2: Graph the coordinates with a smooth curve ▪ On board

7 -5: Exponential Functions �Example 3: y = ¼x �Estimate the value of ¼-1. 5 About 8

7 -5: Exponential Functions �Assignment Page 427 1 – 5, 11 – 19 (odds)

Essential Skills: Graph Exponential Functions Identify behavior that displays exponential functions 7 -5: Exponential Functions Day 2

7 -5: Exponential Functions Exponential y = a ● bx growth Exponent Base (greater than 1) Starting amount (when x = 0) Note that this is the same as any exponential function, except that the base in exponential growth is always greater than 1. Why?

7 -5: Exponential Functions Exponential y = a ● bx Starting amount (when x = 0) Note decay Exponent Base (between 0 and 1) that this is the same as exponential growth, except the base is between 0 and 1. Why?

7 -5: Exponential Functions � 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

7 -5: Exponential Functions �Your Turn 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 ≈ $18, 040

7 -5: Exponential Functions � Example 4 Determine whether the set of data displays exponential behavior. Explain why or why not. x 0 10 20 30 y 10 25 62. 5 156. 25 Look for a pattern ▪ The domain increases by regular intervals of 10 ▪ Look for a common pattern among the range ▪ 10 25 x 2. 5 62. 5 x 2. 5 156. 25 x 2. 5 ▪ Since the range values have a common factor, the equation for the data may involve (2. 5)x, and the data is probably exponential.

7 -5: Exponential Functions �Your Turn Determine whether the set of data displays exponential behavior. Explain why or why not. x 0 10 20 30 y 100 50 25 12. 5 ▪ Yes, the data is exponential ▪ Each range value is being multiplied by 0. 5

7 -5: Exponential Functions �Assignment Page 427 ▪ 7 (part b only), 8, 9 ▪ 20 (part a only), 21 - 24