Math 181 Exam I (Summer 2015/2016) Name: Exam Coverage: Midterm Exam 1 covers material from Units 1-3. Specifically, you should be familiar with topics from chapters 1.1, 1.2, 10.1, 10.2, and 10.3. Exam Availability & Deadlines: This exam is available to download at 8:00am on Monday, July 11, 2016 and is due by 11:59pm (Eastern Time) on Monday, July 18, 2016. Exam Format: When you are ready to take the exam, you should download it, print it, complete it, scan in your solutions, and submit your solutions via any of the methods listed below. The exam is open book and open notes and has a total of 100 possible points. You are allowed to use a calculator; but, you must show all of your work on your exam paper. Answers without proper justification will not receive full credit. You must do all of your own work and cannot ask for help from any other person. If something mentioned in a question is unclear, please email your instructor at aran@drexel.edu for an explanation. Good luck! Exam Submission You may submit your exam by any of the following methods: 1. upload your exam by clicking the blue \"Midterm Exam 1\" link in unit 4. 2. hand it in at Korman 206 (Office of the Math Department) on the main campus, Philadelphia, during regular business hours. If you choose to upload your exam, please write your name on all of the exam pages and keep the problems in order. Remember that your exam should be a pdf file. There is a link for a free pdf converter in the course links section. PLEASE PUT ALL PAGES IN ONE PDF FILE! It is your responsibility to make sure that all pages are included in your exam submission. You should view your submission online to make sure that all pages have uploaded properly. In all email communications (especially when using a non Drexel account), please include your name and Math 181 in the subject line. Late submission of this exam will result in a zero (0) grade for this assignment. Page 1 Math 181 Exam I (Summer 2015/2016) Name: You must solve all problems using methods described in this course; guess and check is not an appropriate method for solving equations. 1. (10 Points) In 1940, there were 248,272 immigrants admitted to a country. In 2004, the number was 1,123,487. (a) Assume that the rate of change of immigration with time is linear. Find a linear function P (t) which can be used to determine the number of immigrants in year t, where t is the number of years after 1900. (b) Use your result in part (a) to predict the number of immigrants admitted to the country in 2014. Page 2 Math 181 Exam I (Summer 2015/2016) Name: 2. (20 Points) Suppose that a company's cost (in thousands of dollars) for selling x units is C(x) = x + 2 and its revenue (in thousands of dollars) from selling x units is R(x) = x2 + 8x 4. (a) How many units must be sold un order to break even? (If there is more than one answer, list all of them.) (b) What is the profit from selling 5 units? (c) How many units must be sold to maximize the revenue? What is the maximum revenue? (d) In order to maximize profit, should the company sell the number of units which maximized its revenue (found in part (c))? Why or why not? (e) Sketch the revenue and cost functions on the same coordinate axes. Label all intercepts with the x and y axes as well as all break-even points. Draw and label a vertical line at the value of x where the revenue is maximized. Page 3 Math 181 Exam I (Summer 2015/2016) Name: 3. (10 Points) Suppose f (x) = x2 3x + 1. Assuming h 6= 0, compute and fully simplify the following quantity: f (x + h) f (x) h Page 4 Math 181 Exam I (Summer 2015/2016) Name: 4. (10 Points) Determine the domain. Express your answer in interval notation. (a) f (x) = x3 x3 x (b) f (x) = x2 7x 8 Page 5 Math 181 Exam I (Summer 2015/2016) Name: 5. (10 Points) The average cost per unit to produce x units of plywood is AC(x) = 300 . x + 10 (a) What is the average cost per unit if 590 units are produced? (b) If the average cost per unit is $1.50, how many units are produced? Page 6 Math 181 Exam I (Summer 2015/2016) Name: 6. (10 Points Find an equation of the line which passes through (12, 39) and (2, 48). Page 7 Math 181 Exam I (Summer 2015/2016) Name: 7. (20 Points) Consider the following figure: (a) Determine the coordinates of the equilibrium point. Express your answer as an ordered pair (q, p). (b) If the price is $25, what is the demand quantity? (c) If the price is $25, what is the supply quantity? (d) Express the price as a function of the supply quantity; that is, determine p = S(q). Page 8 Math 181 Exam I (Summer 2015/2016) Name: 8. (10 Points) For each of the following, write \"True\" if the statement is true or \"False\" if the statement is false. (a) The domain of every polynomial function is (, ). (b) The range of every polynomial function is (, ). (c) There are no lines perpendicular to the line y = 5. (d) A polynomial of degree 3 can have at most 3 turning points. (e) A polynomial of degree 5 does not have a minimum (a smallest y-value). Page 9