NAME:MATH 103 Exam 3, version (a)24 October 2008100 pointsInstructions:1. This exam has 6 pages (including this one), which contain 8 problems and one bonus problem.Please check that you have all of the pages.2. Answer all of the following questions clearly and completely. Justify all of your answers.3. You may not use a book or any notes for this exam.4. Give your answer to each problem completely and clearly in the space provided. You may usethe back of the exam pages for scratch work; however, if you want this work to be considered,make note of it in the space provided for the problem.5. Erase or cross out work you do not wish to be graded.6. Credit, partial or full, will be given only if sufficient steps leading to the answers are shown.7. You have 50 minutes to complete this exam.Page 1Problem 1. (10 points) Be sure to show work for both parts of this problem, even if you can dothem in your head, so that I can see that you understand how to do these conversions and that youaren’t just using your calculator.(a) (5 points) Convert3π4radians to degrees.(b) (5 points) Convert 75◦to radians. Express your answer as a multiple of π (in other words, donot approximate your answer with a decimal).Problem 2. (12 points) Find the exact value of 2 log721 − log79 without using a calculator.Page 2Problem 3. (12 points) Suppose θ is an acute angle and cos θ =4041. Find the values of the otherfive trigonometric functions of θ.Problem 4. (14 points) The function f (x) =42 − xis one-to-one. Find its inverse function f−1and check your answer.Page 3Problem 5. (10 points) Solve5 log(x + 571) = 15.Problem 6. (14 points) You have $850 to invest. What rate of return r, compounded continuously,do you need in order to have $1250 after 6 years?Page 4Problem 7. (16 points) In an electric circuit, the voltage across the terminals of a capacitor whichis discharging through a resistor decays exponentially. In other words, the voltage V (t) at time t isgiven byV (t) = V0ekt,where V0is the voltage at time t = 0. Suppose this capacitor is charged so that the voltage acrossits terminals at time t = 0 is 25 volts. After 10 seconds the voltage is measured and is found to be8 volts.(a) (8 points) Find the value of k in the exponential decay model above.(b) (8 points) What will be the voltage across the terminals of the capacitor at time t = 15 seconds?Page 5Problem 8. (12 points) A ladder is leaning against a wall. The base of the ladder is 4 feet fromthe base of the wall, and the ladder makes an angle of 70.5◦with the floor. How long is the ladder?Bonus problem. (+4 points) There are a few trigonometric functions which were once commonbut are now very rarely used. One of these is called the versine, written versin θ, which is defined asversin θ = 1 − cos θ.Find the exact value of (1 + sin 68◦)(versin 22◦)(csc222◦) without using a calculator.Page