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.
Decay Factor

To find it in a table, take any y-value and
divide it by the previous y-value.

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
 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

Find the Decay Factor and Rate from this table
x
y
0
80
1) Divide a Y value by the
previous value.
2) Repeat with different values.
Are they the same?
1
60
2
45
3) That is your Decay Factor.
3
33.75
4) Convert to a Decay Rate (%)
4
25.3125
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 = .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)
v = $3894.14
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?