## Precalculus Test Out Practice Exam

Part 3 Test 2 Time: 3 hours

1. Determine on what interval(s) the function is decreasing.

2. Identify any asymptotes of the graph of .

3. If you deposit \$5,000 in a trust fund that pays 9.5% interest, compounded continuously, which of the following values is closest to the amount that will be in the trust after 50 years. Rounded to the nearest \$1.00.

4. The population model for a certain town is given by the equation

where t is the time in years, with t=0 corresponding to 1990. What will the population be in 2000?

5. Find the domain of the function .

6. Find the inverse function of the function .

7. Use the properties of logarithms to simplify the expression , and write as a sum difference, and/or constant multiple of logarithms.

8. Evaluate .

9. Solve .

10. Solve .

11. Solve .

12. Solve .

Answer: c) None of the above, because only 6 is in the domain of the original equation.

13. The demand equation for a certain product is given by

Find the demands x for price .

14. How many years will it take your money to double if you deposit it into a fund paying 10% compounded monthly?

15. How many years will it take your money to double if you deposit it into an account paying 10% simple interest?

16. If the half-life of a substance is 500 years, how many years will it take for 60% of the substance to disappear?

17. If bacteria is growing at the rate of 10 cells per second, how long will it take for the culture to reach 1 million cells?

18. Which of the following is a power model?

Answer: e) None of the above.

19. Find the value of b in the exponential function that passes through the points (0,2) and (4,3).

20. Find the range of the function .

21. Find the inverse of the function .

22. Solve the following system of equations for x:

Answer: e) None of the above. x = 2.

23. Solve the following system of equations for y:

24. Find the value of b in the equation of the parabola that passes through the points (0,6), , and .

25. A small corporation borrowed \$800,000 to expand its product line. Some of the money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at 9% if the annual interest was \$67,000 and the amount borrowed at 8% was five times the amount borrowed at 10%.