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

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Presentation transcript:

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

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

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

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

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

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

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

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

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