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Analysis AB

Unit 7 Review

Mrs. Pretz

1. Write the equation for the graphs below.

a.) b.)

c.)

2. Graph the function [pic].

3. Graph the function [pic]

4. Money is invested at 6.5% interest compounded monthly. How long will it take for the investment to double?

5. Use the properties of logarithms to expand [pic].

6. Use the properties of logarithms to expand [pic]

7. Evaluate the following without your calculator:

(a) [pic] (b) [pic]

(c) [pic] (d) [pic]

8. Use your calculator to evaluate the following:

(a) [pic] (b) [pic]

(c) [pic] (d) [pic]

9. Use the properties of logarithms to condense [pic].

10. Use the properties of logarithms to condense [pic]

11. Determine the principal that must be invested at an annual rate of 9% compounded continuously so that the balance in 20 years will be $35,000.

12. Solve the following equations. Give exact solutions first, then use your calculator to approximate.

(a) [pic] (b) [pic]

(c) [pic] (d) [pic]

(e) [pic] (f) [pic]

(g) [pic]

13. Superman has a violent reaction to red kryptonite, which decays into green kryptonite, fortunately with a half-life of 15 hours. It is no longer dangerous to Superman when 90% of the red kryptonite has decayed. If Superman is exposed to pure red kryptonite, for how long is he in danger?

14. Students were given an exam on exponents and logarithms and then tested monthly with an equivalent exam. The average score for the class was given by the human memory model [pic] where t is the time in months. After how many months will the average score be 70?

Answers:

1. a.) [pic]

b.) [pic]

c.)

4. 10.693 years

5. ln 5 + ln x – 1/3 ln(x2 + 1)

6. [pic]

7a. 3

7b. 1/3

7c. 3/5

7d. 3/2

8a. .881

8b. can’t be done

8c. 1.921

8d. 1.404

9. [pic]

10. [pic]

11. $5,785.46

12a. 8/3

12b. -4

12c. [pic]

12d. [pic]≈.093

12e. [pic]

12f. ln 2, ln 3

12g. [pic]

13. 49.8 hours

14. 3.217 months

-----------------------

(1.5, 4)

(1, 5)

(-2, 7)

[pic]

(2, -5)

(-2, -4)

(-2.8, -3)

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