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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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decay factor
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.
decay factor1
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

decay rate
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.
practice
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.
find the equation
Find the Equation

y= 80(.75)x

Decay rate is

1 - .75 = .25 = 25%

find the equation and decay rate
Find the Equation and Decay Rate

y = 192(.5)x

Decay rate is

1 - .5 = .5 = 50%

solve
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

or make a table
Or Make a Table

v = 10,000(.91)n

Why is the Decay

Factor .91 and not .09?