Name: Algebra 2
Date:
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 function
o Given an input-output pair and a multiplier, find the starting value
o Given an exponential function, find the % rate of increase or decrease
o Given a starting amount and another point, find the exponential function and the % rate of increase or decrease
o 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.
Name: Algebra 2
Date:
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7. 51 + 50 + 5 –1
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10. 2 –2 + 4 –2
11. (2 + 4) –2
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Name: Algebra 2
Date:
Part 2 : For Part 2 you should use your calculator.
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 2 nd 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 2 nd 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.
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?
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 3 6. x = 16
3 7. x = 6 3 8. x = 16 3 9. x = -1 4 0. x = 5
4 1. x = -3 4 2. x = -11 4 3. x = 2 4 4. x = 1
45. x = 8
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