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1. (5 pts) Approximate each of the following using a calculator. Express your answer rounded to three decimal places.

a.

b.

c.

d.

2. (5 pts) Beginning with the graph of , use transformations to graph .

3. Solve each equation.

a. (5 pts)

b. (5 pts)

4. (5 pts) Find the domain of .

5. (10 pts) Suppose Use properties of logarithms to write in terms of a and b.

6. This is a 3-part problem:

a. (5 pts) Use factoring to write in lowest terms.

b. (5 pts) Write as a sum and/or difference of logarithms. Express powers as factors.

c. (5 pts) Write as a single logarithm. For full credit, simplify as much as possible.

7. (5 pts) Use the change-of-base formula and a calculator to evaluate .

8. Solve each of the following equations for x. Be sure to check that your answer is in the domain of the original equation.

a. (5 pts)

b. (5 pts) (Hint: Use your answer to part a.)

c. (5 bonus pts) .
(Do NOT use a calculator. Leave your answer in terms of .)

9. (5 pts) Solve . (Hint: This equation is quadratic in .)

10. (5 pts) Answer one of the following word problems:

a. A culture of bacteria obeys the law of uninhibited growth. If 500 bacteria are present initially, and there are 800 bacteria after 3 hours, how many will be present in the culture after 5 hours?

b. The half-life of Carbon-14 is about 5600 years. A piece of charcoal from an ancient fire pit contains 35% of the carbon-14 as is found in living plants of today. How old is the fire pit? (You may (must) assume that plants of yesteryear have about the same amount of radioactive C-14 in them as they do today.)

11. A clever student will anticipate a question or two on the logistic model and Newton’s Law of Cooling to show up, probably as bonus material.