Name __________________________________
Date ___________________
LESSON 7.5
Study Guide
GOAL
Write and graph exponential decay functions.
Vocabulary
When a > 0 and 0 < b < 1, the function y = a · bx represents exponential decay.
EXAMPLE 1
Write a function rule
Tell whether the table represents an exponential function. If so, write a rule for the
function.
The y - values are multiplied by 6 for each increase of 1 in x, so the table represents an
exponential function of the form y = abx with b = 6.
x
–1
0
1
2
y

1
3
–2
–12
–72
The value of y when x = 0 is –2, so a = –2.
The table represents the exponential function y = –2 • 6x.
Exercise for Example 1
1.
Tell whether the table represents an exponential function. If so, write a rule for the
function.
x
–2
–1
0
1
2
y
1
3
9
27
81
EXAMPLE 2
Graph an exponential function
 1 x
Graph the function y =   . Identify its domain and range.
10 
Solution
STEP 1 Make a table of values. The domain is
all real numbers.
x
y
–1
10
0
1
1
1
10
2
1
100
STEP 2 Plot the points.
STEP 3 Draw a smooth curve through the points.
From either the table or the graph, you can see the range is all positive real
numbers.
Name __________________________________
Date ___________________
LESSON 7.5
Study Guide Continued
EXAMPLE 3
Classify and write rules for functions
Tell whether the graph represents exponential growth or exponential decay. Then
write a rule for the function.
a.
b.
Solution
a. The graph represents exponential decay ( y = abx where 0 < b < 1). The yintercept is 15, so a = 15. Find the value of b by using the point (1, 5) and a = 15
y = abx
5 = 15 • b1
1
3 =b
Write function.
Substitute.
Solve.
1  x
A function rule is y = 15 •  
3 
b. The graph represents exponential growth ( y = abx where b > 1). The y-intercept is
4, so a = 4. Find the value of b by using the point (1, 8) and a = 4.
y = abx
8 = 4 • b1
2=b
Write function
Substitute
Solve.
A function rule is y = 4 • 2x.
Exercises for Examples 2 and 3
2.
3.
Graph y = (0.7)x and identify its domain and range.
 1
The graph of an exponential function passes through the points (0, 4) and 1, 
 2
Graph the function. Tell whether the graph represents exponential growth or
exponential decay. Then write a rule for the function.
Answer Key
Lesson 7.5
Study Guide
1. y = 9 p 3x
2.
domain: all real
numbers;
range: all positive real numbers
3.
x
 
exponential decay; y = 4 p  1 
 8