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Exponential Functions

This guide explores the concepts of exponential growth and decay through real-world examples. It details population changes, such as a town of 130,000 growing at 1% annually, and a city of 3 million declining by 1.5% per year. It also examines the decay of the value of a purchased item losing 20% of its value yearly and an investment growing at 4% interest compounded annually. Each example includes the initial value, growth or decay factors, and calculations for future values over specified years.

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Exponential Functions

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  1. Exponential Functions Exponential Growth Exponential Decay Created by: David W. Cummins

  2. A population of 130,000 increases by 1% each year. Initial value? a = 130000 Growth or decay? Growth! b will be greater than 1. Growth factor? b = 100% + 1% = 101% = 1.01 Exponential Equation: y = abx y = (130000)(1.01)x

  3. y = (130000)(1.01)x Find population size in 7 years! x = 7 y = (130000)(1.01)7 y = 139377.5958 Or approximately 139,000

  4. A population of 3,000,000 decreases by 1.5% each year. Initial value? a = 3000000 Decay! Growth or decay? b will between 0 and 1. Decay factor? b = 100% - 1.5% = 98.5% = .985 Exponential Equation: y = abx y = (3000000)(.985)x

  5. y = (3000000)(.985)x Find population size in 5 years! x = 5 y = (3000000)(.985)5 y = 2,781,649.507 Or approximately 2.78 million

  6. An item purchased for $900 has a 20% loss in value each year. a = 900 Initial value? Growth or decay? Decay! b will between 0 and 1. Decay factor? b = 100% - 20% = 80% = .80 Exponential Equation: y = abx y = (900)(.80)x

  7. y = (900)(.80)x Find value in 6 years! x = 6 y = (900)(.80)6 y = 235.9296 Or $235.93

  8. An investment of $3,000 earns 4% interest compounded annually. Initial value? a = 3000 Growth or decay? Growth! b will be greater than 1. Growth factor? b = 100% + 4% = 104% = 1.04 Exponential Equation: y = abx y = (3000)(1.04)x

  9. y = (3000)(1.04)x Find population size in 8 years! x = 8 y = (3000)(1.04)8 y = 4105.707151 Or $4105.71

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