Math 12 (Spring 2001) Kouba Exam 2

Please PRINT your name here :

Your HW/Exam ID Number

1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO.

2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR CO-OPERATION.

3. YOU ARE ENCOURAGED TO USE A CALCULATOR ON THIS EXAM.

4. No notes, books, or classmates may be used as resources for this exam.

5. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.

6. Put units on answers where units are appropriate.

7. You have until 9:50 a.m. sharp to finish the exam.

8. Make sure that you have 5 pages including the cover page.

1.) (2 pts. each) Mark whether each statement is true (T) or false (F). a.) ln 1 = 0 b.) 3 ^{x} · 3 ^{y} = 3 ^{xy} c.) log_{b}(x + y) = log_{b} x + log_{b} y d.) 4^{log_{4} x} = x e.) log e = 1 f.) (ln x)(ln y) = ln(xy) g.) log_{b} 0 = 1 h.) log x − log y = log(x/y) i.) e^{−x} < 0 j.) (log_{b} x)^{y} = y · log_{b} x

2.) (10 pts.) Find the intercepts, vertex, domain, range, and graph for the parabola y = x^{2} − 6x .

3.) (8 pts.) Use a sign chart to determine the domain for the function y = log_{5}(x^{2} − 3x) .

4.) (10 pts.) Sketch the graph of y = −2^{(x+1)} +8 in the following way. Start with the graph of y = 2^{x} then use translations and reflections (both clearly stated) to get the desired graph. Denote the domain, range, intercepts, and asymptotes.

5.) (10 pts.) Consider the rational function f(x) = \frac{2x − 6}{x − 1} . Fill out the

following table of values (to two decimal places) for this function.

....x......2....1.2....1.1....10....100....0....0.8....0.9.... − 1.... − 10.... − 100

f(x)

Determine the domain, range, intercepts, and asymptotes and sketch the graph of this function.

6.) (7 pts.) Use polynomial division to find an equation for the tilted asymp-

tote for the function y = \frac{x^{2} − x + 4}{x + 2} .

7.) (10 pts.) Assume that the numbers of rabbits N in a breeding population is given by N = 15 · 2^{(1/3)t}, where t is time in months.

a.) How many rabbits are there initially (when t = 0 months) ? When t = 9 months ?

b.) In how many months (exact value AND to one decimal place) will there be 450 rabbits ?

8.) (5 pts. each) Solve for x.

a.) 10 ^{3−x} ≤ 4

b.) e^{2x} − e^{x} = 2

c.) ln(x − 2) + ln x = ln 3 9.) (10 pts.) A three-side rectangular pen is built against a wall. If the total length of fencing is 100 feet, what dimensions x and y will result in a pen of maximum area and what will that area be ?

The following EXTRA CREDIT PROBLEM is worth 10 points. This problem is OPTIONAL.

1.) Determine the domain for the function y = \frac{400}{(log x)^{2} − log x^{2}} .