1. Decay at a constant percentage rate can be described by
7-3 Exponential Decay
Big Idea
Decay at a constant percentage
rate can be described by
an expression of the
form bg , where
0 < g < 1 and the
variable is in the exponent. x
Review the exponential growth, constant change, &
exponential decay graphs and equations on p. 415.

2. In 1–3, graph the equation with a graphing calculator. Identify:
Warm-Up
In 1–3, graph the equation with a graphing calculator. Identify:
a. the y-intercept of each graph.
b. three points on the graph.
c. the line that the graph approaches as x becomes very large.
1. y = 100(0.80) y = 21,000(0.85) y = 10(0.97)
x x x
100
21,000 10 30 50
150
a a. 21, a. 10
(1, 80)
(2, 64)
(3, 51.2)
(1, 17850)
(2, )
(3, )
(1, 9.7)
(2, 9.409)
(3, )
c. x-axis c. x-axis c. x-axis

3. bg 120 (1-.15) 120 (.85) 53.244… 53 words x 5 5 Additional Example
1. Assume that each day after cramming, a student forgets 15% of the words known the day before. A student crams for a Spanish test on Thursday by learning 120 vocabulary words on Wednesday night. But the test is delayed from Thursday to Monday. If the student does not study more, how many words is he or she likely to remember on Monday? x bg 5
120 (1-.15) 5
120 (.85)
53.244…
53 words

4. 2. In June 1953, the first Chevrolet Corvette rolled off the
assembly line with a sticker price of approximately $3,000.
Suppose its value depreciated by 9% each year after
production.
a. Find an equation that gives the car’s value y when it is x
years old.
b. What was the predicted value of the car in 1960? How close
is this to the actual price of a 1953 Corvette, which was $1,640,
in 1960?
c. Graph the car’s value for the interval 0 ≤ x ≤ 7.
d. What was the predicted value of the car in 2006? How close
is this to the actual price of a 1953 Corvette, which was
$59,900 in 2006? x
a. y = 3000 · (.91)
c. Next page 7 53
b. y = 3000 · (.91)
d. y = 3000 · (.91)
y = $
y = $20.24
1640 – = $89.72
59900 – = $

5. y
3100
3000
2900
2800
2700
2600
2500
2400
2300
2200
2100
2000
1900
1800
1700
1600
1500 c.  x y
3000 1
2730 2
2484 3
2261 4
2057 5
1872 6
1704 7
1550
Value ($)   Z x
Age of Car

6. 3. Caffeine is a drug found in a wide variety of food products
consumed by Americans. In fact, more than half of all adult
Americans consume at least 300 milligrams of caffeine every day. Once in the body, it takes about 6 hours for half of the caffeine to be eliminated. Suppose the pattern of eliminating caffeine from the body continues after it is ingested at one time; that is, half of the remaining caffeine is eliminated every 6 hours.
a. Write an equation to describe y, the amount of caffeine in the
bloodstream after x six-hour periods have passed.
b. Make a calculator table for the equation from Part a. Use the
table to find when approximately 1 milligram of caffeine
remains in the body.
c. How much caffeine remains after 108 hours?
d. According to the equation, when will the
amount of caffeine in the body be zero? b. x y 1 2 3 4 5 6
300
150 75
37.5
18.75
9.375
4.6875 x
a. y = 300 · .5
c. (x = 108 ÷ 6 = 18) 18
y = 300 · .5
y = .001 mg
x = 0
d. Never