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8-1 Exploring Exponent Models

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 ,

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8-1 Exploring Exponent Models

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  1. 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.

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

  3. 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.

  4. 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.

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

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

  7. 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.

  8. 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 -0.35 = -r subtracting 1 from both sides 0.35 = r multiplying both sides by -1 So the percent of decrease is 35%

  9. 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)

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