Name: ______
Studio College Algebra – Exam 3
April 3, 2012
1. Rewrite the formula by taking the natural logarithm of both sides. Simplify answer completely.
2. Rewrite the formula by taking the natural logarithm of both sides. Simplify answer completely.
3. If and, what is ?
4. Solve .
5. Solve .
6. What lump sum would you need to invest at 10.00% interest compounded monthly so that your investment will be worth $20,000 after 18 years? Round your answer to the nearest cent.
7. The supply function for a certain product is given by , where p is the price of the product in dollars, and q is the quantity supplied at that price. If the price for the product is $72,900, what quantity, q, will be supplied?
8. On the grid to the right, sketch a polynomial with the following properties:
· 4th degree
· negative leading coefficient
· double root at
· single root at
· single root at
9. Find 2 different 4th degree polynomials with single roots at and , and a double root at . You do not need to multiply your answers out.
Answer 1: ______
Answer 2: ______
10. What are all the real and complex roots of the polynomial 2x3 + 24x2 + 98x + 136, given that one root is x = -4?
11. What are all the real and complex roots of the polynomial 2x3 − 6x2 + 108, given that one root is
x = -3?
12. Given the polynomial , answer the following questions:
a) What is the leading coefficient of f(x)?
b) What is the degree of f(x)?
c) What is the constant term of f(x)?
d) As (fill in the blank).
e) As (fill in the blank).
13. Suppose the revenue function for a certain product is given by , where x is the number of units sold, and R(x) is in dollars. For what values of x will there be zero dollars in revenue?
14. What is the domain of the function ? Show all work.
15. What is the horizontal asymptote of the function ? Explain how you arrived at the answer.
16. For each of the functions below, state whether the function represents ‘exponential growth’ or ‘exponential decay.’
a) ______
b) ______
c) ______
d) ______
e) ______
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