Math 1320 Exam 1 Review T. Johnson September 23, 2014 Exam Date: 9/30/2014 – in class, no scantron or bluebook necessary This review is similar to your exam. Complete it to the best of your ability and on your own as much as possible. You will NOT have notes, people, books, etc. when exam day comes. For the exam you are only to use a writing implement (pen or pencil, no highlighters) and a calculator. You may NOT share a calculator and a phone is not a calculator. 1. Let f  x   2 x  3 . Evaluate the following. 2. 3. 4. 5. a. f(2) b. f(-1) c. 3f(4) – 2f(-2) Your college newspaper has fixed production costs of $70 per edition and marginal printing and distribution costs of 40¢ per copy. The paper sells for 50¢ per copy. a. Find the associated cost function. b. Find the associated revenue function. c. Find the associated profit function. d. How many copies should be sold to break-even? Find a linear equation whose graph is a straight line through (2, -4) and (1, 1). A soft-drink manufacturer can produce 1000 cases of soda in a week at a total cost of $6000, and 1500 cases of soda at a total cost of $8,500. Find the manufacturer’s weekly cost function. Given the demand function q  3 p  300 , a. Express the total revenue R as a function of price p per item. b. Determine the price p that maximizes revenue. c. What is the maximum revenue? 6. The annual net income of General Electric for 2007 – 2012 could be approximated by P  t   3.0t 2  24t  59 billion dollars where t is time in years since 2005. a. According to the model, in what year was General Electric’s net income lowest? b. What was the net income in that year? c. Would you trust this model to continue to be valid long past 2012? Why? 7. Soon after taking an Aleve ™, a patient has absorbed 400 mg of the drug. If the amount of Aleve™ in the bloodstream decays exponentially, with half being removed every 15 hours, find the time it will take for the amount of Aleve ™ in the bloodstream to decrease to 160 mg. Round your answer to one decimal place. 8. Two functions are given in the table. One is linear, y  mx  b , and the other is exponential, y  A  b  . In the blanks provided, identify the type of function and then find the equation. x x f(x) g(x) -2 -1 0 1 2 5 10 20 40 80 5 2 -1 -4 -7 The function f(x) is ____________________ with equation f  x   ____________________ (linear or exponential) The function g(x) is ___________________ with equation g  x   ______________________ 9. Complete the table. Exponential 34  81 Logarithmic 23  2 1 8 log100  2 1   9 3 log7 49  2 10. For the function given by Q  x   17e0.7398 x , rewrite in the form f  x   A  b  . x Solutions (Updated 9/28) 1. a) f(2) = -1 b) f(-1) = 5 c) 3f(4) – 2f(-2) = 3(-5) – 2(7) = -29 2. a) C(x) = 0.40x+70 b) R(x) = 0.50x c) P(x) = 0.10x-70 d) x = 700 copies 3. y = -5x + 6 4. Points: (1000,6000) and (1500,8500) Cost function: C(x) = 5x + 1000 5. a) R  p   3 p 2  300 p b) p = $50 c) R(50) = $7500 6. a) t = 4 so the year is 2009 b) $11 billion c) No, answers vary. 7. 19.8 hours 8. f(x) is exponential (multiply/divide to get next y) with f  x   20  2  x g(x) is linear (add/subtract to get next y) with g(x) = -3x – 1 9. Exponential 34  81 23  Logarithmic log3 81  4 1 log 2    3 8 10. f  x   17  0.4772  x 1 8 102  100 72  49 log100  2 log7 49  2 2 1   9 3 log1/3  9   2