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4.1 and 4.2 Exponential Functions

𝑓(𝑥) = 𝑎 ∙ 𝑏𝑥−ℎ + 𝑘

GRAPH:

1) State whether the following functions model exponential growth of exponential decay.

2) Graph the following functions.

3) State the Domain and Range.

4) Identify the y-intercept and asymptote.

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Example: The value of a snowmobile has been decreasing by 7% each year since it was new. After 3 years, the

value is #3000. Find the original cost of the snowmobile.

Example: In 1996, there were 2573 computer viruses and other computer security incidents. During the next 7

years, the number of incidents increased by about 92% each year. Write an exponential growth model giving the

number n of incidents t years after 1996. About how many incidents were there in 2015? Estimate the year

when there were about 125,000.

Bank G: Interest Compounded Weekly

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4.3 The Number e

4

5

4.4 Logarithmic Functions

Graphing:

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25. Galloping Speed Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times. An animal that is galloping has all four feet off the ground at times. The number S of strides per minute at which an animal breaks from a trot to a gallop is

related to the animal's weight w (in pounds) by the model S = 256.2 47.9 log w. Approximate the number of strides per minute for a 450 pound horse when it breaks from a trot to a gallop.

26. Tornadoes The wind speed S (in miles per hour)

near the center of a tornado is related to the distance d (in miles) the tornado travels by the model S = 93

log d + 65. Approximate the wind speed of a tornado

that traveled 75 miles.

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4.5-4.6

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Word Problems:

4. You put $5000 in the bank in a savings account that makes 2% annual interest. After how many years will there be $8000

in the account if the account is compounded monthly?

5. You put $5000 in a savings account that makes 2% interest compounded continuously.

a. How much money do you have after 8 years?

b. How many years does it take until the account has $10,000 in it?

6. If you borrow $5000 for 5 years at 9% annual interest, how much INTEREST will you pay on the loan if interest is

compounded quarterly?

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7. Bob invests $200 into an account that is compounded continuously at an interest rate of 3%. How much money will he

have after 2 years?

8. Each day, 15% of the chlorine in a swimming pool evaporates. After how many days will 60% of the chlorine have

evaporated? (Careful of the %)

9. You are collecting cats. You collect them exponentially at an annual growth rate of 124%. If you started with only 2 cats,

how many cats do you have after 10 years?

10. Radium is stored in a container. The amount R (in grams) of radium present after t years can be modeled by 0.00043tR Pe . What is the initial amount of radium if after 1057 years there are only 3 grams left?

Solve.

11. 0232 xx ee 14 .

42

1

93

1

x

x

10

Graph the function. State the domain and range.

1. y = 3 • 2x – 3 2. y = 3

4

x

Simplify the expression.

4. 4e3 • e5 5. (–4e2x)3

6.5

24

xe

e 7.

6

4

9

3

x

x

e

e

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Graph the function. State the domain and range.

8. y = 3ex 9. y = 2e–4x

10. You deposit $3000 in an account that pays 5% annual interest

compounded continuously. What is the balance after 2 years?

Evaluate the logarithm without using a calculator.

11. log2 8 12. log6 1

13. log5 5 14. log1/3 27

Graph the function. State the domain and range.

15. y = log5 x 16. y = In x + 3

Expand the expression.

17. log3 4x 18. In 4x2y5

Condense the expression.

19. log5 24 – log5 6 20. log8 6 + 2 log8 3

Use the change-of-base formula to evaluate the logarithm.

21. log4 12 22. log9 18

23. The sound of a barking dog has an intensity of I = 10–4 watts per square meter. Use the model L(I ) = 10 log 0

I

I where

Io = 10–12 watts per square meter, to find the barking dog’s loudness L(I).

Solve the equation.

24. 3x+1 = 27x + 3 25. ex = 5

26. 23x + 9 = 25 27. 4x + 1 – 7 = 14

28. log6 (5x + 8) = log6(13x) 29. In (4x – 2) = In(8x)

30. 9 In x = 54 31. log3(x + 7) = 3

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