Name: Algebra 2Date:

Review for Test on Exponents, Logs, and Exponential Functions

You will be responsible for the following topics:

Exponent properties Negative exponents Fraction exponents Simplifying expressions using exponent properties (including fraction and negative exponents) Simplifying expressions with logarithms Solving equations with exponents and logarithms Exponential modeling (word problems):

o Given a % rate of increase or decrease, find and use an exponential functiono Given an input-output pair and a multiplier, find the starting valueo Given an exponential function, find the % rate of increase or decreaseo Given a starting amount and another point, find the exponential function and the % rate of

increase or decreaseo Given a starting value, multiplier, and output, find the exponent

Review Problems:Part 1-Simplify the following. Do not use your calculator for Part 1.

1.

2.

3.

4.

5.

6.

7. 51 + 50 + 5 –1

8.

9.

10. 2 –2 + 4 –2

11. (2 + 4) –2

Name: Algebra 2Date:

12.

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Name: Algebra 2Date:

27.

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36.

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37.

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Part 2: For Part 2 you should use your calculator.

Name: Algebra 2Date:1. Marta has a savings account that pays 1.5% interest annually. She has not made any deposits or withdrawals for many years. Suppose that her current balance is $4,516.32. How much money was in her account 5 years ago? Show how you get your answer.

2. Of all the users of the web service Twitter, Lady Gaga (@ladygaga) has the most followers. At the start of year 2010, she had 3,200,000 followers. Her number of followers has been steadily increasing by 8% each month.

a. Let f(x) stand for how many followers @ladygaga has, x months after the start of year 2010. Write a function formula for f(x).

b. How many followers did @ladygaga have at the start of 2011?

c. Solve graphically using the 2nd trace-intersect function on your calculator or by algebra using logarithms. Round your answer to two decimal places. When did the number of followers of @ladygaga surpass 5,000,000 ?

d. Solve graphically using the 2nd trace-intersect function on your calculator or by algebra using logarithms. Round your answer to two decimal places Solve the equation f(x) = 10,000,000. Explain the meaning of the answer as it relates to @ladygaga on Twitter.

3. Giovanna has a bank certificate that pays 2.25% interest monthly. (Increases by 2.25% each month) She does not make any additional deposits or withdrawals. Her current balance is $6,543.21.

Name: Algebra 2Date:

a. How much was this certificate worth 2 years ago?

b. How much will the certificate be worth, 10 months from now?

4. Mrs. Chang owns a painting whose value has been growing exponentially. In the 6 years she’s owned the painting, its value has grown from $20,000 to $30,000.

By about what percent did the painting’s value grow each year?

5. Mrs. Jones owns a painting whose value has been decreasing exponentially. In the 12 years she’s owned the painting, its value has decreases from $40,000 to $10,000.

By about what percent did the painting’s value decrease each year?

6. Mr. Patrick owns a classic car whose value has been increasing by 3.5% each year. The car is worth $5000. He wants to sell the car when it is worth $10,000. How many years must he wait?

Name: Algebra 2Date:Answers:

Part 1:

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

13. 14. 15. 16.

17. 18. 19. 20.

21. 22. 1 23. 24.

25. 26. 15 27. -4 28. 0

29. 11/2 30. -6 31. 9 32. -8

33. 6 34. -1/2 35. 1/2 36. x = 16

37. x = 6 38. x = 16 39. x = -1 40. x = 5

41. x = -3 42. x = -11 43. x = 2 44. x = 1

45. x = 8

Name: Algebra 2Date:Part 2:

1. 4516.32 · (1.015)–5 = 4192.32, so the balance 5 years ago was $4,192.32.

2. a.

b. f(12) ≈ 8,058,144 so a little over 8 million followers

c. The graphs of Y1=3200000 · 1.08x and Y2= 5000000 intersect at x ≈ 5.8, so it took about 5.8 months from the start of the year, meaning that it happened in late June 2010.

d. Same method as part c, x ≈ 14.8, so it took about 14.8 months from the start of 2010, so around late-March 2011, for Lady Gaga to have 10,000,000 followers.

3. a.

b.

4.

So, the value of the painting grew by 6.991% per year or about 7% per year.

5.

So the painting’s value decreased by about 10.9% per year

6. Y1=

Y2=10,000

x=20.15 years