Math 1050-1
Name:
Exam 2
Student ID#
To receive full credit, you must show all of your work. Write your answer in the space
provided. Please box your answer and keep your work neat and organized. You may not use a
calculator, notes, or any other electronic devices. Unless specified you do not need to simplify
your answers. Relax, enjoy, and no cheating.
Problem Score
1
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4
5
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8
1. (5 points) The total revenue R earned (in dollars) from producing a gift box of candles is given by
R(p) = −10p2 + 800p
where p is the price per unit (in dollars). Find the unit price that will yield a maximum revenue.
2. (5 points) Write
3 + 2i
in standard form which is a + bi where a and b are real numbers.
5+i
3. Let f (x) = x3 + 2x2 − 5x − 6.
(a) (5 points) List all of the possible rational zeros of f (x).
(b) (5 points) Using synthetic division, test to see if x = 3 is a zero of f (x), and explain your answer.
(c) (5 points) Find all of the zeros of f (x).
(d) (1 point) Write the polynomial f (x) as the product of linear factors.
4. (10 points) Let
f (x) =
x3 − 2x2 − 5x + 6
(x − 1)(x + 2)(x − 3)
=
.
x2 + 5x + 4
(x + 1)(x + 4)
(a) Find the vertical asymptotes (if any).
(b) Find the horizontal asymptotes (if any).
(c) Find the slant (or oblique) asymptotes (if any).
5. (5 points) Find all the values of x which satisfy the following:
x−5
≤ 0.
3−x
Graph your solution on the real number line.
6. (5 points) Find the exact value of log5 75 − log5 3.
7. (5 points) Solve the following equation:
ln(x2 − 3x) = ln(3 − 5x).
Make sure you check your answer(s).
8. (5 points) You deposit $5000 into an account that pays 7.25% interst, compounded continuously. How
long will it take for the money to triple?