Answers for the following questions:

Exponential and Logarithmic functions; Solving polynomials

1. Which of the following is equal to log_6?(t+1)?-log_6?(t^2-1)?

2. Why do we use the Intermediate Value and Bisection Theorems to find only the irrational roots of polynomials?

3. If 2-i is a root of 3x^3-11x^2+11x+5, then what are its other roots?

4. On which interval does the Intermediate Value Theorem guarantee that the polynomial x^4+7x^2-9x-1 has a root?

5. Which of the following is the conclusion you can draw using Descartes Rule of Signs applied to 2x^4-6x^3+x^2+7x-4?

6. Find all roots of x^3+2x^2+2x+1. Hint: find the rational one(s) first.

7. Recall that the pH of a solution is given by the formula log c, where c is the concentration of H+ in gram-ions per liter. Find the pH when that concentration is 5.310)^(-7).

8. Which of these is the remainder when 4x^4-5x^3+9 is divided by x-3?

9. Which of the following is a reason for why the trace function on a graphing calculator can sometimes be better than the bisection theorem for finding roots?

10. Which of the following is not a property of logarithms?

11. If P(x) is a polynomial with P(-6) = -1.12 and P(-5) = 0.6 then which of the following must be true?

12. In 10 years, 25% of a radioactive substance decays. What is its half-life?

13. Is it possible for a degree-4 polynomial P(x) to have only complex (no real) roots?

14. A falling object has a velocity 37(1-e^(-0.4t)) meters per second after t seconds of free fall. Which of the following statements is true?

15. How long will it take a population with 10% annual growth rate to double?

16. Which of these is a factor of 2x^100-x^7-1?

17. If 1 and -6 are two of the roots of 6x^4+31x^3-33x^2-16x+12, then what are the other two?

18. Write ln(?ab/?c) in terms of ln a, ln b, and ln c. You may assume that all variables are positive.

19. Which is better for the investor, an investment that pays 2% annual interest compounded monthly or an investment that pays 2.1% interest annually?

20. How many roots does x^6=3x^5+1 have?

21. Solve 2^x=5^(x^2) for x.

22. Use the Rational Roots Theorem to list all possible rational roots of 24x^3+2x-7.

23. If a business depreciates its photocopiers to a percent P of their original cost after n years using double-declining, the formula that they use to do so is n=log P/log 0.8 . What percentage of its original value does a copier have after 5 years?

24. Which of these graphs could be the graph of y=e^x+1?

25. A population of 2000 snakes is released into a marshland and grows according to the formula P = 2000(1.5)^t, where t is the number of months after the release. Find the population 10 months after the release.