1. Chapter 10.1 Exponential Functions Standard & Honors
Algebra II Mr. Gilbert
Chapter 10.1
Exponential Functions
Standard & Honors
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2. Agenda
Warm up
Decay project
Lesson
Homework
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3. Homework Review
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4. Communicate Effectively
Asymptote: a line on a graph approached but never crossed.
Radical number:
Exponent
Exponential Function: y=2x
Growth: y=abx| a 0, b>1
Decay: y=abx | a 0, 0<b<1
Examples of Exponential Functions:
Population growth, Interest Income growth,
radioactive decay: m(t)=m0ekt where m0 is the original amount and t is time, k varied by element.
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5. World Population Growth
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6. Example 1 Graph an Exponential Function (3)
Example 2 Identify Exponential Growth and Decay (3)
Example 3 Write an Exponential Function (5)
Example 4 Simplify Expressions with Irrational Exponents (3)
Example 5 Solve Exponential Equations (4)
Example 6 Solve Exponential Inequalities (3)
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Lesson 1 Contents

7. x Sketch the graph of . Then state the function’s domain and range.
Make a table of values. Connect the points to sketch a smooth curve. 16 2 4 1 –1 –2 x
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Example 1-1a

8. Answer:
The domain is all real numbers, while the range is all positive numbers.
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Example 1-1b

9. Sketch the graph of Then state the function’s domain and range.
Answer:
The domain is all real numbers; the range is all positive numbers.
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Example 1-1c

10. Determine whether represents exponential growth or decay.
Answer: The function represents exponential decay, since the base, 0.7, is between 0 and 1.
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Example 1-2a

11. Determine whether represents exponential growth or decay.
Answer: The function represents exponential growth, since the base, 3, is greater than 1.
Determine whether represents exponential growth or decay.
Answer: The function represents exponential growth,
since the base, is greater than 1.
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Example 1-2b

12. Answer: The function represents exponential decay, since the
Determine whether each function represents exponential growth or decay. a. b. c.
Answer: The function represents exponential decay, since the base, 0.5, is between 0 and 1.
Answer: The function represents exponential growth, since the base, 2, is greater than 1.
Answer: The function represents exponential decay, since the
base, is between 0 and 1.
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Example 1-2d

13. Cellular Phones In December of 1990, there were 5,283,000 cellular telephone subscribers in the United States. By December of 2000, this number had risen to 109,478,000.
Write an exponential function of the form that could be used to model the number of cellular telephone subscribers y in the U.S. Write the function in terms of x, the number of years since 1990.
For 1990, the time x equals 0, and the initial number of cellular telephone subscribers y is 5,283,000. Thus the y-intercept, and the value of a, is 5,283,000.
For 2000, the time x equals 2000 – 1990 or 10, and the number of cellular telephone subscribers is 109,478,000.
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Example 1-3a

14. Replace x with 10, y with 109,478,000 and a with 5,283,000.
Substitute these values and the value of a into an exponential function to approximate the value of b.
Exponential function
Replace x with 10, y with 109,478,000 and a with 5,283,000.
Divide each side by 5,283,000.
Take the 10th root of each side.
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Example 1-3b

15. To find the 10th root of 20. 72, use selection
To find the 10th root of 20.72, use selection under the MATH menu on the TI-83 Plus.
ENTER
MATH
Keystrokes: 10
Answer: An equation that models the number of cellular telephone subscribers in the U.S. from 1990 to is
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Example 1-3c

16. For 2010, the time x equals 2010 – 1990 or 20.
Suppose the number of telephone subscribers continues to increase at the same rate. Estimate the number of US subscribers in 2010.
For 2010, the time x equals 2010 – 1990 or 20.
Modeling equation
Replace x with 20.
Use a calculator.
Answer: The number of cell phone subscribers will be about 2,136,000,000 in 2010.
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Example 1-3d

17. Health In 1991, 4. 9% of Americans had diabetes
Health In 1991, 4.9% of Americans had diabetes. By 2000, this percent had risen to 7.3%.
a. Write an exponential function of the form could be used to model the percentage of Americans with diabetes. Write the function in terms of x, the number of years since 1991.
b. Suppose the percent of Americans with diabetes continues to increase at the same rate. Estimate the percent of Americans with diabetes in 2010.
Answer:
Answer: 11.4%
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Example 1-3e

18. Simplify .
Quotient of Powers
Answer:
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Example 1-4a

19. Simplify . Power of a Power Product of Radicals Answer: 9/21/2018
Example 1-4b

20. Simplify each expression. a.b.
Answer:
Answer:
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Example 1-4c

21. Rewrite 256 as 44 so each side has the same base.
Solve .
Original equation
Rewrite 256 as 44 so each side has the same base.
Property of Equality for Exponential Functions
Add 2 to each side.
Divide each side by 9.
Answer: The solution is
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Example 1-5a

22. Check Original equation Substitute for n. Simplify. Simplify.
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Example 1-5b

23. Rewrite 9 as 32 so each side has the same base.
Solve .
Original equation
Rewrite 9 as 32 so each side has the same base.
Property of Equality for Exponential Functions
Distributive Property
Subtract 4x from each side.
Answer: The solution is
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Example 1-5c

24. Solve each equation. a. b.
Answer:
Answer: 1
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Example 1-5d

25. Property of Inequality for Exponential Functions
Solve
Original inequality
Rewrite as
Property of Inequality for Exponential Functions
Subtract 3 from each side.
Divide each side by –2.
Answer: The solution is
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Example 1-6a

26. Check: Test a value of k less than for example,
Original inequality
Replace k with 0.
Simplify.
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Example 1-6b

27. Solve
Answer:
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Example 1-6c

28. Homework - Honors See Syllabus 10.1
pp : (multiples of 3), 57-67
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29. Homework See Syllabus 10.1 pp. 528-529: 21-54 (multiples of 3), 57-61
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