Exponential Decay

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

x y
0 80
1 40
2 20
3 10
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

x y
0 80
1 60
2 45
3 33.75
4 25.3125

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 ()
5. Subtract from 1.
6. Convert to percent.

6
Find the Equation
x y
0 80
1 60
2 45
3 33.75
4 25.3125
y 80(.75)x
Decay rate is 1 - .75 .25 25
7
Find the Equation and Decay Rate
x y
0 192
1 96
2 48
3 24
4 12
5 6
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
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?