Exam 2 Answer Sheet - Precalculus | MATH 115, Exams of Pre-Calculus

Download Exam 2 Answer Sheet - Precalculus | MATH 115 and more Exams Pre-Calculus in PDF only on Docsity! NAME ________________________ October 31,1991 ID ______________ SECTION ____ _ 4 MATH 115 EXAM 2 INSTRUCTIONS: Write your name, ID number, and section number on this test sheet and each of the answer sheets. Number the answer sheets from 1 to 6. Answer Problems 1-6 on the answer sheets as indicated and Problem 7 on this sheet. If a problem asks for an exact answer, algebraic methods must be used to obtain the answer (and the work must be shown); a calculator approximation will not receive full credit if an exact answer is requested. Do not give decimal approximations for fractions. You must return this exam sheet in order to receive a grade for this test. You must show all appropriate work in order to receive credit for an answer. Read the exam carefully. Mark your answers clearly. Good luck! Answer Problem 1 on Answer Sheet 1. 1 . a. Find the value of each of the logarithms in parts i and ii below accurate to 4 decimal places. Show clearly how you arrived at your answer. i. log [(72,654)482 ] ii. Iog 12 583 b. Suppose Iog5 b = -.24, Iog5 c = 3.2. Find the exact value of each of the quantities in parts iii-v without using the change of base formula. Show clearly how you arrived at your answer . (5,5,3) iii. Iog5 25 iy - logs be v. c Answer Problem 2 on Answer Sheet 2. f/x\ + Q+Q_Q 2. Suppose f is a polynomial with x-intercepts -3, -2, 1, and 5 and i f the table of signs shown on the right. Draw a graph for the "3 -2 polynomial f described above and find a polynomial function that could have that graph. Answer Problem 3 on Answer Sheet 3. 3. Howard P. Feebleblaster has discovered a new mold which seems to thrive in his coffee cup. On Tuesday at 10 a.m. there was 0.1 pound of mold in his cup. Fifty hours later (at noon on Thursday) the mold in his cup weighed 1 pound. Assume that the mold was growing exponentially. (4) a. Write a function that gives the amount of mold after t hours. (6) b. When would the weight of the mold equal Howard's 150 pounds? Write an appropriate equation and solve algebraically. Then state your answer to the nearest hour (either as a total number of hours or as a certain number of days and hours). Answer Problem 4 on Answer Sheet 4. (g) 4. Answer either part a or part b. a. Clarence Mouse sees a piece of cheese that is at the center of a fenced area. If the cheese is at the 1 1x y point (0,0), then the equation for the fence's location is x + Q = ^' wnere me units are in feet. Clarence fears that the fenced area is a trap so he wants to reach the cheese without going inside the fence. If he has a pole that is 2.5 feet long, can Clarence reach the cheese? Explain your reasoning including why he cannoi; reach the cheese from any point along the fence or where he should stand in order to reach the cheese if he can reach it. b. Goofy wants to build a parabolic arch. On paper he has drawn the parabola with the x-axis as its axis of symmetry, its vertex at the point (10, 0). The parabola passes through the point (0,5). What is the equation of the parabola that Goofy drew? Answer Problem 5 on Answer Sheet 5. do 5. Solve algebraically the inequality: 15 - 4x1 < 3 Answer Problem 6 on Answer Sheet 6. 6. Find all solutions for each of the following equations (exact values): (lo.io) a. ln(3x-5)-ln(5x + 7)==0 b. 45x = Please turn over for Problem 7 4 page i of 2 Answer Problem 7 on this page. x - 507. a. Let g(x) = . nnn j - Find each of the following for g (give exact values) and then draw the T-V/V/W — OL/X — X graph of g. The graph must show all vertical and horizontal asymptotes and any x- and y- intercepts. Asymptotes must be clearly labeled with their equations and intercepts with their values. The graph should indicate clearly the behavior of the function on each of the intervals determined by the intercepts and asymptotes The x-intercept(s) of the graph: The y-intercept of the graph: The vertical asymptote(s) of the graph: The horizontal asymptote: The table of signs for g (5) x-50 b. Use the table of signs to solve the inequality ———————~ < 04000 - 60x - xz A—page 2 of 2