1. DO NOW HW: Exponential Functions Worksheet
Warm-Up: What is the formula for compound interest? What is different about the formula for exponential decay?

2. Exponential Functions
Review Jeopardy

3. Linear, Quad., or Exp.
Growth & Decay 2
Analyze the Equation
Growth & Decay
Geometric Sequences 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5

4. Analyze for 1
Question: Does the following equation represent growth or decay
y = 100(1.06)x
Check Your Answer

5. Analyze for 1
Answer:
Back to the Game Board

6. Analyze for 2
Question: What is the starting amount in the equation below?
y = 2450(.86)x
Check Your Answer

7. 2450
Analyze for 2
Answer:
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8. Analyze for 3
Question:
Identify the initial amount and the growth factor:
y = 250(1.065)x
Check Your Answer

9. Analyze for 3
Answer:
Initial amount: 250
Growth factor:
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10. Analyze for 4
Question:
What is the percent growth?
y = 5(1.02)x
Check Your Answer

11. Analyze for 4
Answer:
Back to the Game Board

12. Analyze for 5
Question: The equation below represents the value of Caleb’s savings account. y = 500(1+ (.08/12))12(16)
How much money did he start with?
What is the percent interest he earns?
How often is it compounded?
How many years is it compounded for?
Check Your Answer

13. Analyze for 5 Back to the Game Board Answer:
How much money did he start with?
$500
What is the percent interest he earns? 8%
How often is it compounded?
monthly
How many years is it compounded for? 16
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14. Growth & Decay for 1 Check Your Answer
Question: A $25000 purchase decreases 12% in value each year. Determine the value of the purchase after 7 years using the equation y = 25000(.88)xAbsolute Value
Check Your Answer

15. $10,216.89
Growth & Decay for 1
Answer:
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16. Growth & Decay for 2
Question: A town with a population of 5,000 grows 3% each year. Find the population at the end of 10 years.
Check Your Answer

17. Growth & Decay for 2 y = 5000(1.03)10 6,720 (rounded) Answer:
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18. Growth & Decay for 3 Check Your Answer
Question: Carbon-14 has a half-life of 5,700 years. Suppose the average page of a book containing approximately 8 mg is put into a time capsule. How much carbon-14 will each page contain after 22,800 years? Write the equation and give your answer.
Check Your Answer

19. Growth & Decay for 3
Answer:
y = 8(.5)4
.5 mg
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20. Growth & Decay for 4
Question: A piece of equipment costs $75,000 new but depreciates 12% per year in each succeeding year. Find its value after 8 years.
Check Your Answer

21. Growth & Decay for 4
Answer:
y = 75000( )8 $
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22. Growth & Decay for 5 Question: Check Your Answer
Find the value of $1000 deposited for 8 years in an account paying 8% annual interest compounded semiannually.
Check Your Answer

23. Growth & Decay for 5
Answer:
y = 1000 (1 + (.08/2))2(8) $
Back to the Game Board
Check Your Answer

24. Growth & Decay for 1 Back to the Game Board Check Your Answer
Question:
There are 5,000 fish in the pond and the population is increasing by 2.1% each year. Using the equation y = 5000(1.021)x, how many fish will there be after 15 years?
Back to the Game Board
Check Your Answer

25. Growth & Decay for 1
Answer:
6829 fish (rounded)
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26. Growth & Decay for 2 Check Your Answer Question:
Write an exponential function to model the situation. Then estimate the value of the function after 5 years (to the nearest whole number).
A population of 290 animals that increases at an annual rate of 9%.
Check Your Answer

27. Growth & Decay for 2 Answer: Back to the Game Board y = 290(1 + .09)5
446 animals
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28. Growth & Decay for 3 Check Your Answer Question:
The population of fish in the pond (with no predators) doubles every day. If the pond started with 5 fish, how many would there be after 8 days if the pattern continues.
Check Your Answer

29. Growth & Decay for 3
Answer:
y = 5(2)8
1280 fish
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30. Growth & Decay for 4 Check Your Answer
Question: Write an exponential function to model the situation. Then estimate the value of the function after 5 years (to the nearest whole number).
A population of 220 animals that decreases at an annual rate of 19%.
Check Your Answer

31. Growth & Decay for 4
Answer:
y = 220( )5
77 animals
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32. Growth & Decay for 5 Question: Check Your Answer
Find the value of $1000 deposited for 10 years in an account paying 6% annual interest compounded monthly.
Check Your Answer

33. Growth & Decay for 5
Answer:
y = 1000 (1 + (.06/12))12(10) $
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34. Linear, Quad., Exp for 1
Question:
Check Your Answer

35. Linear, Quad., Exp for 1
Answer:
linear
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36. Linear, Quad., Exp for 2 Question: y = 7x2 +5x – 2 WHY?
Check Your Answer

37. Linear, Quad., Exp for 2 Answer: Quadratic Has an x squared
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38. Linear, Quad., Exp for 3 Question: WHY? Check Your Answer X -1 1 2 3 Y1 2 3 Y 16 4
1/16
Check Your Answer

39. Linear, Quad., Exp for 3 Answer:
Exponential – multiplies by ¼ each time
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40. Linear, Quad., Exp for 4 Check Your Answer
Question: The table shows the body temperature of a desert spiny lizard at various air temperatures. Write the equation that fits the best
Air Temp, A (ºC) 26 27 28 29 30
Body Tem (ºC)
33.44
33.78
34.12
34.46
34.80
Check Your Answer

41. Linear, Quad., Exp for 4 Answer: Linear y = .34x + 24.6
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42. Linear, Quad., Exp for 5 Check Your Answer Period, t(sec) 1 2 3 4 5
Question: The time it takes for a clock’s pendulum to swing from one side to another and back again is called the pendulums period. The table shows the period of a pendulum of length l. Write the equation that best fits the data. Round to the nearest hundredth.
Period, t(sec) 1 2 3 4 5
Length, l (ft)
0.81
3.28
7.4
13.12
20.4
Check Your Answer

43. Linear, Quad., Exp for 5 Answer: Quadratic is best y=.8x2 + .09x - .09
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44. Geometric Sequences for 1
Question:
Find the next three terms of the sequence:
4, 12, 36, 108…
Check Your Answer

45. Geometric Sequences for 1
Answer:
540, 1620, 4860
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46. Geometric Sequences for 2
Question:
What is the common ratio in the sequence:
2, -8, 32, -128
Check Your Answer

47. Geometric Sequences for 2
Answer:
r = -4
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48. Geometric Sequences for 3
Question:
What is the common ratio in the sequence:
-100, -40, -16, -6.4
Check Your Answer

49. Geometric Sequences for 3
Answer:
.4 or 2/5
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50. Geometric Sequences for 4
Question:
Is the following sequence geometric?
-0.2, -0.02, ,
Check Your Answer

51. Geometric Sequences for 4
Answer:
Yes, the common ratio is .1 or 1/10
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52. Geometric Sequences for 5
Question:
Write a rule for the sequence:
1, 4, 16, 64
Check Your Answer

53. Geometric Sequences for 5
Answer:
NEXT = 4NOW
A(n)=1(4)n-1
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