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Exponential Decay

Exponential Decay. Decay Factor. The constant factor that each value in an exponential decay pattern is multiplied by to get the next value. Decay factor = the base in an exponential decay equation, y = a(b x ). Example: y = 15(.25 x ) .25 is the decay factor.

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Exponential Decay

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  1. Exponential Decay

  2. Decay Factor • The constant factor that each value in an exponential decay pattern is multiplied by to get the next value. • Decay factor = the base in an exponential decay equation, y = a(bx). • Example: y = 15(.25x) • .25 is the decay factor. • The decay factor is always less than 1.

  3. Decay Factor • To find it in a table, take any y-value and divide it by the previous y-value. • Example: 40 divided by 80 = .5 20 divided by 40 = .5 10 divided by 20 = .5 The decay factor is .5

  4. Decay Rate • Factor to Decay rate - subtract the decay factor from 1. • Example: Decay factor is .25 so the decay rate is 1 - .25 = .75 or 75%. • Decay Factors are ALWAYS less than one (1) • They are NOT negative.

  5. Practice • Find the Decay Factor and Rate from this table • Divide a Y value by the previous value. • Repeat with different values. Are they the same? • That is your Decay Factor. • Convert to a Decay Rate (%) • Subtract from 1. • Convert to percent.

  6. Find the Equation y= 80(.75)x Decay rate is 1 - .75 = .25 = 25%

  7. Find the Equation and Decay Rate y = 192(.5)x Decay rate is 1 - .5 = .5 = 50%

  8. Solve How much is a car worth in 10 years if the value decays at 9% per year? The initial value is $10,000. Equation v = 10,000(.91)n Insert 10 for the variable n v = 10,000(.91)10 v = 10,000 (.389414118) v = $3894.14

  9. Or Make a Table v = 10,000(.91)n Why is the Decay Factor .91 and not .09?

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