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Graph:

1. (5 pts)

2. (5 pts)

3. (4 pts) Determine which of the following functions are one-to-one. Indicate by writing “Yes” or “No” on the graphs.

4. (10 pts) Solve

5. (10 pts) Write an exponential function to model the situation. Tell what each variable represents. A population of red ants is initially at 100,000 ants and grows (exponentially) at 20% per week.

6. (5 pts) Write the equation in exponential form.

7. (5 pts) Evaluate .

8. (10 pts) Express in terms of logarithms of x, y, and z.

9. (10 pts) Solve correct to four decimal places:

10. (5 pts) Solve:

11. (5 pts) Find the value of the expression:

12. (5 pts) Graph:

13. (5 pts) Write the following as the logarithm of a single expression. Assume that variables represent positive numbers.

14. (5 pts) The population (in millions of people) of Soretoothistan t years after 2000 is given by . If there are 12 million people in Soretoothistan in 2005, find k.

15. Cobalt-60 is a radioactive substance that decays according to the model , where A = A(t) is the amount of cobalt-60 present at time t (in years).

a. (5 pts) Find the half-life of cobalt-60. You may leave your final answer in terms of .

b. (5 pts) To the nearest 10th of a year, what is the half-life of cobalt-60, according to this model? (Base your answer on your result from part a.)

16. (10 pts bonus) The half-life of carbon-14 is (approximately) 5730 years.

a. Find an exponential model that gives the amount of radioactive carbon-14 present in a charcoal sample after t years.

b. How old is a sample from a neolithic fire pit if it is found that 19% of naturally-occurring carbon-14 is present in the sample?

17. (5 pts) Solve the equation: .