Exponential Decay Decay Factor The constant factor that

Exponential Decay

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

Decay Factor n To find it in a table, take any y-value and divide it by the previous y-value. n Example: x 0 1 2 3 y 80 40 20 10 40 divided by 80 =. 5 20 divided by 40 =. 5 10 divided by 20 =. 5 The decay factor is. 5

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

Practice n Find the Decay Factor and Rate from this table x y 0 80 1 60 2) Repeat with different values. Are they the same? 2 45 3) That is your Decay Factor. 3 33. 75 4) Convert to a Decay Rate (%) 4 25. 3125 1) Divide a Y value by the previous value. 1) Subtract from 1. 2) Convert to percent.

Find the Equation x y 0 80 1 60 2 45 3 33. 75 4 25. 3125 y= x 80(. 75) Decay rate is 1 -. 75 =. 25 = 25%

Find the Equation and Decay Rate x y 0 192 1 96 2 48 3 24 4 12 5 6 y= x 192(. 5) Decay rate is 1 -. 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 (. 389414118)

Or Make a Table x y 0 10, 000 1 9100 2 8281 3 753. 71 4 6857. 49 5 6240. 32 6 5678. 69 7 5167. 61 8 4702. 53 9 4279. 30 10 3894. 16 v = 10, 000(. 91)n Why is the Decay Factor. 91 and not. 09?