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(bx). Example: y = 15(.25x).25 is the decay factor. The decay factor is always less than 1.

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

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

Practice Find the Decay Factor and Rate from this table Find the Decay Factor and Rate from this table xy )Divide a Y value by the previous value. 2)Repeat with different values. Are they the same? 3)That is your Decay Factor. 4)Convert to a Decay Rate (%) 1)Subtract from 1. 2)Convert to percent.

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

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

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 ( ) v = $

Or Make a Table xy 010, v = 10,000(.91) n Why is the Decay Factor.91 and not.09?