Exponential Growth and Decay Formula:
Initial Starting Value
# of times it grows or decays
y  ab
x
Growth/Decay Rate
Exponential Growth
y  ab
x
b

1
growth rate
1  rate as a decimal 
$10 is invested in a savings account where is grows
5% per year.
y  (10)(1  0.05)
x
100
90
80
y  10(1.05)
x
70
60
50
What is the y –intercept?
Would y = 10(1.5)x be above
or below this graph?
40
30
20
10
10
20
30
40
50
Exponential Decay
y  ab
x
1  rate as a decimal 
0decay
 brate
1
10 grams of a particular liquid decays at a rate of
75% per day.
11
y  (10)(1  0.75)
y  10(0.25)
x
10
9
8
x
7
6
5
4
3
2
1
1
2
3
4
5
Practice: Monthly benefits for Social Security in
May 1992 were $23,307 million. Since then,
benefits have increased about 5.4% per year.
a) Write an exponential function to model the growth of
monthly Social Security benefits paid each year. (use millions
in your answer!)
y = 23,307(1+0.054)x  y = 23,307(1.054)x
b) If benefits continue to grow at this rate, when will the
monthly Social Security benefits reach $50,000 million?
50,000 = 23,307(1.054)x
1)Graph y = 23,307(1.054)x
and y = 50,000
2) Solve 2.14527 = 1.054x
through guess and check
In 1984, funds for the Emergency Food Assistance
program were about $1,075 million. Since 1984,
this fund has decreased about 19% per year.
a) Write an exponential function to model this situation.
Y= 1,075(1 - 0.19)x  y = 1,075(0.81)x
There is 81% of the fund LEFT each year
b) Estimate the funds available for the Emergency Food
Assistance program this year.
Y = 1075(0.81)24  6.839 million
Or graph the equation and TRACE with x = 24