1. Exponential Growth vs. Exponential Decay

2. Exponential Growth vs. Decay
Exponential Decay
y = a∙bx
y = a∙bx
b < 1
b > 1 2 ∙2 ∙2 ∙2 ∙½ ∙½ ∙½
getting bigger
getting smaller

3. Growth or Decay…Why? Growth Decay Decay Growth y = 5 ·2 x

4. Exponential Decay y = 500 · 0.65x # years IPOD
500 1
325 2
211.25 3
137.31 4
89.25 5
58.02 6
37.71 7
24.51 8
15.93 9
10.36 10
6.73
The value of an IPOD decreases at 35% per year. This can be modeled by the function
y = 500 · 0.65x
Make a table of values to find the value of your IPOD for the domain
{0,1,2,3,4,5,6,7,8, 9,10}
Graph your function

5. Decay Factor The population decreased by 13% per year.
100% - 13% = 87%
0.87
Calculating Decay Factor
Identify the percent of decrease.
Subtract the percent from 100%
Change to a decimal.

6. Find the decay factor that you would use if the percent decrease was…
25%
100% - 25%
75%
0.75 3%
100% - 3%
97%
0.97
70%
100% - 70%
30%
0.30
2.6%
100% - 2.6%
97.4%
0.974
4.75%
100% %
95.25%
0.9525

7. Exponential Decay Function
y = a · bx
Starting Value (a)
Suppose the acreage of forest is decreasing by 2% per year because of development. If there are currently 4,500,000 acres of forest, determine the amount of forest land after 5 years.
a = 4,500,000
Decay Factor (b) 2%
100% - 2%
98%
0.98
Exponential Decay Function
y = a · bx
y = 4,500,000 ·0.98 x
4,067,
After 5 Years
y = 4,500,000 ·0.98 5