8-1 Exploring Exponent Models Objectives:  To identify exponential growth and decay.  To define the asymptote  To graph exponential functions  To find.

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Presentation transcript:

8-1 Exploring Exponent Models Objectives:  To identify exponential growth and decay.  To define the asymptote  To graph exponential functions  To find the percent increase or decrease.

Exponential Function A function with the general form y = ab x, where x is a real number, a ≠ 0, b > 0 and b ≠ 1. example: y = 4(2) x

Growth Factor  When b > 1, b is the growth factor example: y = 2(3) x b = 3 which is greater than 1 so it is the growth factor and the function is one of exponential growth. b = 3 which is greater than 1 so it is the growth factor and the function is one of exponential growth.

Decay Factor  When b < 1, b is the decay factor example: y = 2(¼) x b = ¼ which is less than 1 so it is the decay factor and the function is one of exponential decay. b = ¼ which is less than 1 so it is the decay factor and the function is one of exponential decay.

Asymptote  A line that a graph approaches as x or y increases in absolute value.

Graphing Example: Graph y = 2 x. make a table make a table x2x2x y

Percent Increase or Decrease  The growth factor, b > 1, can be represented as b = 1 + r where r is the rate of increase.  The decay factor, b < 1, can be represented as b = 1 – r, where r is the rate of decrease.

example: Find the percent increase or decrease. 1) y = 2(1.3) x b = 1.3 which is > 1 so it is an increase (exponential growth). so b = 1 + r 1.3 = 1 + r substituting 1.3 for b 0.3 = r subtracting 1 from both sides So the percent of increase is 30% 2) y = 0.35(0.65) x b = 0.65 which is < 1 so it is a decrease (exponential decay). so b = 1 - r 0.65 = 1 - r substituting 0.65 for b = -r subtracting 1 from both sides 0.35 = r multiplying both sides by -1 So the percent of decrease is 35%

Class Work 8-1 Sketch the graph of each function. 1. y = (0.8) x 2. y = (¼ ) x Without graphing, determine whether each equation represents exponential growth or decay. 3. y = 15(7) x 4. y = 1285(0.5) x Write an exponential function for a graph that includes the given points. 5. (0, 0.5), (1, 3) 6. (-1, 5), (0.5, 40)