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1 Name: Section: About This Exam: This practice exam is designed to help you prepare for the upcoming exam. The types of questions seen in this practice exam are representative of what you will see on the actual exam. However, there could be content on the actual exam that is not included in the practice exam. You will benefit the most from this exam by treating it like a real exam. You should study all the material before attempting the exam. When you do attempt the practice exam allow yourself 50 minutes and only your calculator and a writing utensil. You will be expected to show all your work and provide justification where necessary on the actual exam. Disclaimer: This practice test DOES NOT serve as an indication of the contents of the actual test. It only suggests a possible format. Page: Total Points: Score: 1

2 True or False Answer the following questions by choosing true or false and clearly filling in exactly one choice. No credit will be given for choices not clearly marked. 1. (5 points) The derivative of any constant function is (5 points) Given the function v(x), if v (2) = 3, then v(x) must be increasing over the interval [2.9, 3.1]. 3. (5 points) If d(t) represents the distance a car has traveled in miles after t hours, then d (t) represents the instantaneous rate of change at time t. 4. (5 points) The rate of change of an exponential function is a constant percent change. 5. (5 points) As x increases to 100, the value of f(x) = 1/x becomes smaller and smaller. This means that lim f(x) = 0. x (5 points) The revenue function R is given by the sum of an items price, p, and the quantity sold, q. Multiple Choice Answer the following questions by choosing a single answer and clearly marking that choice. No credit will be given for choices not clearly marked. 7. (5 points) The function A(t) = 2.15(1.001) t models the amount of money in an account, in millions dollars, where t is years since Which of the following is true? According to this model the account is growing at a annual rate of 100.1%. According to this model the account is decaying at a annual rate of 100.1%. According to this model the account growing at a annual rate of 0.1%. According to this model the account is decaying at a continuous rate of 0.1%. According to this model the account is growing at a continuous rate of 0.1%. According to this model the account is growing at a continuous rate of 100.1%. 2

3 8. (5 points) Given the function f(x), which of the following correctly interprets the meaning of the statement f (x) > 0 for all values of x. f(x) is increasing over its entire domain. f (x) is increasing over its entire domain. f(x) is decreasing over its entire domain. f (x) is decreasing over its entire domain. f(x) is both increasing and decreasing over its entire domain. f (x) is both increasing and decreasing over its entire domain. None of the above answers are correct. 9. (5 points) The function P (t) provides the profit of a large corporation, in billions, t days after the start of the year. Which of the following is the correct interpretation of P (t) = 5.6. lim t At the start of the year the company has a profit of 5.6 billion dollars. The company s profit is growing at a rate of 5.6 dollars per day. As time goes on the company s profit eventually approaches 5.6 billion dollars. The company s profit eventually reaches 5.6 billion dollars. The rate of the growth of company s profit eventually reaches 5.6 billion dollars per day. 10. (5 points) Circle the plot below that correctly plots the tangent line of f(x) at x = 4. 3

4 Short Answer For the following question show all your work. Make sure your answers include any relevant units. No credit will be given for answers without the appropriate amount of work shown. 11. Determine each of the following limits, if they exist. Briefly justify each of your answers. If a limit does not exist write DNE. (a) (2 points) lim t 2 q(t) (b) (6 points) lim h 0 b(4 + h) b(4) h where b(x) = 2x

5 12. Sales of digital books increased rapidly in last ten years. The plot below gives the sales of books, S(t), in millions, t years after (a) (4 points) Estimate S (6). Clearly show your work. (b) (4 points) Explain what your answer from part (a) means in terms of sales of books and time. 13. (7 points) To produce kayaks a small business has fixed costs of $4,000, variable costs of $150, and will sell each kayak for $400. Determine the minimum amount of kayaks the company needs to sell to earn a profit. 5

6 14. Bauer textiles hired a research company to provide supply and demand data for a new product. The research company provided the following functions which each give the quantity as a function of price in dollars. D(p) = 2, 000p + 150, 000 S(p) = 1200p (a) (5 points) Given the information above determine the equilibrium price. (b) (5 points) At what price is the demand 100,000? 15. (5 points) Use the plot of g (x) to fill out the table below. For each value of x choose either increasing, decreasing, or neither for the behavior of g(x) at that point. x g(x)(increasing, decreasing, or neither) 6

7 16. A bank offers an annual interest rate of 2.012% for a new savings account. (a) (6 points) What is the doubling time of the account? (b) (6 points) If you would like your savings account to be worth $4,000 after 5 years, how much do you need to invest now? 7