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• HW: Exponential Functions Worksheet

• Warm-Up: What is the formula for compound interest? What is different about the formula for exponential decay?

Analyze the Analyze the EquationEquation

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Growth & Growth & DecayDecay

Growth & Growth & Decay 2Decay 2

Linear, Linear, Quad., or Quad., or

Exp.Exp.

Geometric Sequences

Question: Does the following equation represent growth or decay

y = 100(1.06)x

Check Your Answer

Analyze for 1

Answer:

Back to the Game Board

Analyze for 1

Growth

Question: What is the starting amount in the equation below?

y = 2450(.86)x

Check Your Answer

Analyze for 2

2450

Answer:

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Analyze for 2

Question:

Identify the initial amount and the growth factor:

y = 250(1.065)x

Check Your Answer

Analyze for 3

Answer:

Initial amount: 250

Growth factor: 1.065

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Analyze for 3

Question:

What is the percent growth?

y = 5(1.02)x

Check Your Answer

Analyze for 4

Answer:

Back to the Game Board

Analyze for 4

%2

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

Analyze for 5

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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Analyze for 5

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

Growth & Decay for 1

$10,216.89

Answer:

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Growth & Decay for 1

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

Growth & Decay for 2

y = 5000(1.03)10

6,720 (rounded)

Answer:

Back to the Game Board

Growth & Decay for 2

Check Your Answer

Growth & Decay for 3Question: 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.

Answer:

y = 8(.5)4

.5 mg

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Growth & Decay for 3

Check Your Answer

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.

Answer:

y = 75000(1 - .12)8

$26972.59

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Growth & Decay for 4

Check Your Answer

Growth & Decay for 5

Question: Find the value of $1000 deposited for 8 years in an account paying 8% annual interest compounded semiannually.

Answer:

y = 1000 (1 + (.08/2))2(8)

$1872.98

Check Your Answer

Growth & Decay for 5

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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

Growth & Decay for 1

Check Your Answer

Answer:

6829 fish (rounded)

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Growth & Decay for 1

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

Growth & Decay for 2

Answer:y = 290(1 + .09)5

446 animals

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Growth & Decay for 2

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

Growth & Decay for 3

Answer:

y = 5(2)8

1280 fish

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Growth & Decay for 3

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

Growth & Decay for 4

Answer:

y = 220(1 - .19)5

77 animals

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Growth & Decay for 4

Question:

Find the value of $1000 deposited for 10 years in an account paying 6% annual interest compounded monthly.

Check Your Answer

Growth & Decay for 5

Answer:

y = 1000 (1 + (.06/12))12(10)

$1819.40

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Growth & Decay for 5

Question:

Check Your Answer

Linear, Quad., Exp for 1

Answer:

linear

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Linear, Quad., Exp for 1

Question:

y = 7x2 +5x – 2

WHY?

Check Your Answer

Linear, Quad., Exp for 2

Answer:

Quadratic

Has an x squared

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Linear, Quad., Exp for 2

Check Your Answer

Linear, Quad., Exp for 3

Question:

WHY?

X -1 0 1 2 3

Y 16 4 1 ¼ 1/16

Answer:

Exponential – multiplies by ¼ each time

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Linear, Quad., Exp for 3

Question: The table shows the body temperature of a desert spiny lizard at various air temperatures. Write the equation that fits the best

Check Your Answer

Linear, Quad., Exp for 4

Air Temp, A (ºC) 26 27 28 29 30

Body Tem (ºC) 33.44 33.78 34.12 34.46 34.80

Answer:

Linear

y = .34x + 24.6

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Linear, Quad., Exp for 4

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.

Check Your Answer

Linear, Quad., Exp for 5

Period, t(sec) 1 2 3 4 5

Length, l (ft) 0.81 3.28 7.4 13.12 20.4

Answer:

Quadratic is best

y=.8x2 + .09x - .09

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Linear, Quad., Exp for 5

Question:

Find the next three terms of the sequence:

4, 12, 36, 108…

Check Your Answer

Geometric Sequences for 1

Answer:

540, 1620, 4860

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Geometric Sequences for 1

Question:

What is the common ratio in the sequence:

2, -8, 32, -128

Check Your Answer

Geometric Sequences for 2

Answer:

r = -4

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Geometric Sequences for 2

Question:

What is the common ratio in the sequence:-100, -40, -16, -6.4

Check Your Answer

Geometric Sequences for 3

Answer:

.4 or 2/5

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Geometric Sequences for 3

Check Your Answer

Geometric Sequences for 4

Question:

Is the following sequence geometric?

-0.2, -0.02, -0.002, -0.0002

Answer:

Yes, the common ratio is .1 or 1/10

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Geometric Sequences for 4

Question:

Write a rule for the sequence:

1, 4, 16, 64

Check Your Answer

Geometric Sequences for 5

Answer:

NEXT = 4NOW

A(n)=1(4)n-1

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Geometric Sequences for 5