1. 1. Evaluate 1 2 3
ANSWER 1 8
2. Evaluate 1 4 –2
ANSWER 16

2. 3. The table shows how much money Tess owes after w weeks
3. The table shows how much money Tess owes after w weeks. Write a rule for the function.
Week, w 1 2 3
Owes, m 50 45 40 35
ANSWER
m = 50 – 5w

3. EXAMPLE 1
Write a function rule
Tell whether the table represents an exponential function. If so, write a rule for the function. x y –1 1 2 3 9 +1 a.

4. EXAMPLE 1
Write a function rule
The y-values are multiplied by 3 for each increase of 1 in x, so the table represents an exponential function of the form y = abx with b = 3.
The value of y when x = 0 is , so a = . 1 3
The table represents the exponential function y = x. 1 3

5. EXAMPLE 1
Write a function rule x y –1 2 1 +1 4 16 b. 1 4
The y-values are multiplied by for each increase of 1 in x, so the table represents an exponential function of the form y = abx with b = .

6. EXAMPLE 1
Write a function rule
The value of y when x = 0 is 1, so a = 1. 1 4
The table represents the exponential function y = x

7. 5 1 GUIDED PRACTICE for Example 1
Tell whether the table represents an exponential function. If so, write a rule for the function. 1 5 x y –1 2 25
ANSWER
yes; y = ( )x 1 5

8. EXAMPLE 2
Graph an exponential function
Graph the function y = x and identify its domain and range. 1 2
SOLUTION
STEP 1
Make a table of values. The domain is all real numbers. 1 2 4 y
– 1
– 2 x

9. EXAMPLE 2
Graph an exponential function
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.

10. Compare graphs of exponential functions
EXAMPLE 3
Compare graphs of exponential functions 1 2 x 1 3 1 2 x
Graph the functions y = and y = −
Compare each graph with the graph of y = 1 2 x

11. EXAMPLE 3
Compare graphs of exponential functions
SOLUTION
= x 1 2 y 3
= ∙ x – x –2 –1
= 3 ∙ 4 12 6

12. EXAMPLE 3
Compare graphs of exponential functions 1 2
Because the y-values for y = x are 3 times the
corresponding y-values for y = x, the graph of
y = x is a vertical stretch of the graph of y = x.
Because the y-values for y = x are times the
y = x is a vertical shrink with reflection in the
x-axis of the graph of y = x. 1 2 1 2 1 2 1 3 1 2 1 3 – – 1 2 1 3 2 – 1 2

13. GUIDED PRACTICE
for Examples 2 and 3
Graph the function y = (0.4)x and identify its domain and range. 2.
ANSWER
Domain: all real numbers
Range: all positive real numbers

14. GUIDED PRACTICE
for Examples 2 and 3
Graph the functions y = 5 (0.4)x. Compare graph with the graph of y = (0.4)x. 3.
ANSWER
The graph is a vertical stretch of y = (0.4)x.

15. Classify and write rules for functions
EXAMPLE 4
Classify and write rules for functions
Tell whether the graph represents exponential growth or exponential decay. Then write a rule for the function.
SOLUTION
The graph represents exponential growth (y = abx where b > 1). The y-intercept is 10, so a = 10. Find the value of b by using the point (1, 12) and a = 10.
y = abx
Write function.
12 = 10  b1
Substitute.
1.2 = b
Solve.
A function rule is y = 10(1.2)x.

16. Classify and write rules for functions
EXAMPLE 4
Classify and write rules for functions
Tell whether the graph represents exponential growth or exponential decay. Then write a rule for the function.
The graph represents exponential decay (y = abx where 0 < b < 1).The y-intercept is 8, so a = 8. Find the value of b by using the point (1, 4) and a = 8.
y = abx
Write function.
4 = 8  b1
Substitute.
0.5 = b
Solve.
A function rule is y = 8(0.5)x.

17. GUIDED PRACTICE
for Example 4
4. The graph of an exponential function passes through the points (0, 10) and (1, 8). Graph the function. Tell whether the graph represents exponential growth or exponential decay. Write a rule for the function.
ANSWER
exponential decay; y = 10  (0.8)x

18. EXAMPLE 5
Solve a multi-step problem
FORESTRY
The number of acres of Ponderosa pine forests decreased in the western United States from 1963 to 2002 by 0.5% annually. In 1963 there were about 41 million acres of Ponderosa pine forests. a.
Write a function that models the number of acres of Ponderosa pine forests in the western United States over time.

19. Solve a multi-step problem
EXAMPLE 5
Solve a multi-step problem
To the nearest tenth, about how many million acres of Ponderosa pine forests were there in 2002?
SOLUTION a.
Let P be the number of acres (in millions), and let t be the time (in years) since The initial value is 41, and the decay rate is
P = a(1 – r)t
Write exponential decay model.
= 41(1 – 0.005)t
Substitute 41 for a and for r.
= 41(0.995)t
Simplify.

20. Solve a multi-step problem
EXAMPLE 5
Solve a multi-step problem
To the nearest tenth, about how many million acres of Ponderosa pine forests were there in 2002?
P = 41(0.995)
Substitute 39 for t. Use a calculator.
ANSWER
There were about 33.7 million acres of
Ponderosa pine forests in 2002.

21. GUIDED PRACTICE
for Example 5
WHAT IF? In Example 5, suppose the decay rate of the forests remains the same beyond About how many acres will be left in 2010? 5.
There will be about 32.4 million acres of Ponderosa pine forest in 2010.
ANSWER

22. ( ) Daily Homework Quiz x 1 1. Graph y = 3 ANSWER
( ) x
ANSWER
2. The population in a town has been declining at a rate of 2% per year since The population was 84,223 in What was the population in 2006?
ANSWER
about 76,130