1. Splash Screen

2. You graphed polynomial functions. (Lesson 6–4)
Graph exponential growth functions.
Graph exponential decay functions.
Then/Now

3. exponential function exponential growth asymptote growth factor
exponential decay
decay factor
Vocabulary

4. Concept

5. Graph of y = 4x. State the domain and range.
Graph Exponential Growth Functions
Graph of y = 4x. State the domain and range.
Make a table of values. Connect the points to sketch a smooth curve.
Example 1

6. Graph Exponential Growth Functions
Answer:
The domain is all real numbers, and the range is all positive real numbers.
Example 1

7. Which is the graph of y = 3x?
A. B.
C. D. A B C D
Example 1

8. Concept

9. A. Graph the function y = 3x – 2. State the domain and range.
Graph Transformations
A. Graph the function y = 3x – 2. State the domain and range.
The equation represents a translation of the graph y = 3x down 2 units.
Example 2A

10. Domain = {all real numbers} Range = {y│y > –2}
Graph Transformations
Answer:
Domain = {all real numbers}
Range = {y│y > –2}
Example 2A

11. B. Graph the function y = 2x – 1. State the domain and range.
Graph Transformations
B. Graph the function y = 2x – 1. State the domain and range.
The equation represents a translation of the graph y = 2x right 1 unit.
Example 2B

12. Domain = {all real numbers} Range = {y │y ≥ 0}
Graph Transformations
Answer:
Domain = {all real numbers}
Range = {y │y ≥ 0}
Example 2B

13. A. Graph the function y = 2x – 4.
A. B.
C. D. A B C D
Example 2A

14. B. Graph the function y = 4x – 2 + 3.
A. B.
C. D. A B C D
Example 2B

15. First, write an equation using a = 1.020 (in billions), and r = 0.195.
Graph Exponential Growth Functions
INTERNET In 2006, there were 1,020,000,000 people worldwide using the Internet. At that time, the number of users was growing by 19.5% annually. Draw a graph showing how the number of users would grow from 2006 to 2016 if that rate continued.
First, write an equation using a = (in billions), and r =
y = 1.020(1.195)t
Then graph the equation.
Example 3

16. Graph Exponential Growth Functions
Answer:
Example 3

17. CELLULAR PHONES In 2006, there were about 2,000,000,000 people worldwide using cellular phones. At that time, the number of users was growing by 11% annually. Which graph shows how the number of users would grow from 2006 to 2014 if that rate continued?
A. B.
C. D. A B C D
Example 3

18. Concept

19. A. Graph the function State the domain and range.
Graph Exponential Decay Functions
A. Graph the function State the domain and range.
Example 4A

20. Domain = {all real numbers} Range = {y│y > 0}
Graph Exponential Decay Functions
Answer:
Domain = {all real numbers}
Range = {y│y > 0}
Example 4A

21. B. Graph the function State the domain and range.
Graph Exponential Decay Functions
B. Graph the function State the domain and range.
The equation represents a transformation of the graph of
Examine each parameter.
● There is a negative sign in front of the function: The graph is reflected on the y-axis.
● a = 4: The graph is compressed.
Example 4B

22. ● h = 1: The graph is translated 1 unit right.
Graph Exponential Decay Functions
● h = 1: The graph is translated 1 unit right.
● k = 2: The graph is translated 2 units up.
Answer:
Domain = {all real numbers}
Range = {y│y < 2}
Example 4B

23. A. Graph the function
A. B.
C. D. A B C D
Example 4A

24. B. Graph the function
A. B.
C. D. A B C D
Example 4B

25. Graph Exponential Decay Functions
A. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in2 at Earth’s surface. It decreases by about 20% for each mile of altitude up to about 50 miles. Draw a graph to represent atmospheric pressure for altitude from 0 to 20 miles.
y = a(1 – r)t
= 14.7(1 – 0.20)t
= 14.7(0.80)t
Example 5A

26. Graph the equation. Answer: Graph Exponential Decay Functions
Example 5A

27. y = 14.7(0.80)t Equation from part a.
Graph Exponential Decay Functions
B. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in2 at Earth’s surface. It decreases by about 20% for each mile of altitude up to about 50 miles. Estimate the atmospheric pressure at an altitude of 10 miles.
y = 14.7(0.80)t Equation from part a.
= 14.7(0.80)10 Replace t with 10.
≈ 1.58 lb/in2 Use a calculator.
Answer: The atmospheric pressure at an altitude of about 10 miles will be approximately lb/in2.
Example 5B

28. A. AIR PRESSURE The pressure of a car tire with a bent rim is 34
A. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in2 at the start of a road trip. It decreases by about 3% for each mile driven due to a leaky seal. Draw a graph to represent the air pressure for a trip from 0 to 40 miles.
A B.
C D. A B C D
Example 5A

29. B. AIR PRESSURE The pressure of a car tire with a bent rim is 34
B. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in2 at the start of a road trip. It decreases by about 3% for each mile driven due to a leaky seal. Estimate the air pressure of the tire after 20 miles.
A lb/in2
B lb/in2
C lb/in2
D lb/in2 A B C D
Example 5B

30. End of the Lesson