Section 11-2 Graphs of Exponential Functions Objective: Students will be able to 1. Graph exponential functions and inequalities 2.Solve real life problems.

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Graph of Exponential Functions

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Section 11-2 Graphs of Exponential Functions Objective: Students will be able to 1. Graph exponential functions and inequalities 2.Solve real life problems involving exponential growth and decay.

Exponential Function: Characteristics of the graphs of y = b x, (Parent Graph) Domain : All real numbers. Range: y > 0 Y-Intercept: (0, 1) Horizontal Asymptote: y = 0 Graph will rise from left to right, b > 1 Graph will fall from left to right, b < 1

Example 1: Graph the exponential functions y = 3 x, y = 3 x + 2, and y = - 3 x on the same set of axes. Compare and contrast the graphs. Hor. Asy.: y = 0 Hor. Asy.: y = 2Hor. Asy.: y = 0 What will happen to the graph if b < 1? Graph will go downward from left to right. Domain: R Range: y > 0 Domain: R Range: y > 2 Domain: R Range: y < 0

Example 2: PHYSICS A ball is dropped from a height of 20 meters on to pavement. On each bounce, the ball bounces to a height that is 40% less than its height on the previous bounce. The height of the ball can be modeled by the equation y = 20(0.6) t, where y is the height of the ball in meters, and t is the number of times the ball bounces. a. Find the height of the ball after its fourth bounce. b. Graph the height function. Height of the ball after 4 bounces is about 2.6 m. x y x y Each box = 4

Exponential Growth or Decay: Example 3: POPULATION Between 1990 and 2000, the population of Florida had an annual growth rate of about 2.14%. If the state’s population was 12,937,926 in 1990, approximately what was Florida’s population in 2000? Compound Interest: Many real-life problems involve quantities that increase and decrease over time. If it increases it is called exponential growth and decreases is exponential decay. Car: decreases over time Home: increases over time Florida’s population in 2000 was about 15,989,070. P: Principal(Initial investment) r : is the annual interest rate n : number of times interest is paid or calculated t : time in years

Example 4: FINANCE Determine the amount of money in a savings account providing an annual rate of 3% compounded daily if Sandra made a one-time deposit of $8500 in to the account and left it there for 5 years. Sandra has about $ in her account after 5 years.

Example 5: Graph the following inequality. Horizontal translation 1 rt. Vertical Dialation, expanded by 4 Vertical translation 3 down Horizontal Asymptote: y = -3 Domain: All Real Numbers Range: y > -3