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. To find it in a table, take any y-value and divide it by the previous y-value. Example: xy 080 140 220 310 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. 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%. Example: Decay factor is.25 so the decay rate is 1 -.25 =.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.

5. Practice Find the Decay Factor and Rate from this table Find the Decay Factor and Rate from this table xy 080 160 245 333.75 425.3125 1)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.

6. Find the Equation xy 080 160 245 333.75 425.3125 y= 80(.75) x Decay rate is 1 -.75 =.25 = 25%

7. Find the Equation and Decay Rate xy 0192 196 248 324 412 56 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 xy 010,000 19100 28281 3753.71 46857.49 56240.32 65678.69 75167.61 84702.53 94279.30 103894.16 v = 10,000(.91) n Why is the Decay Factor.91 and not.09?