Math 103: College Algebra and TrigonometryExam 3 review problemsProblem 1. The function f (x) = x3+ 5 is one-to-one. Find its inverse function and checkyour answer.Problem 2.(a) Graph the function f(x) = 3x.(b) Use your graph from part (a) to graph the function g(x) = 3−x.(c) Use your graph from part (b) to graph the function h(x) = 3−x− 2.Problem 3. Solve 3x2· 27x= 99.Problem 4. What is the domain of the function f(x) = ln x?Problem 5. What is the domain of the function f (x) = log281(x2+ 4x − 5)? [Hint: Youwill need to solve a polynomial inequality.]Problem 6. Find the exact value of 3 log122 + log1218 without using a calculator. [Youcan use a calculator to check your answer, of course.]Problem 7. Solve log2(x + 1) + log2(x + 3) = 3. Check your answer. [Remember to makesure your solutions are in the domain of both log2(x + 1) and log2(x + 3) so that they reallyare solutions to the original equation. You might have to discard solutions that aren’t inthe domain.]Problem 8. You invest $1000 at 5% compounded semiannually (twice a year). How longwill it take until you have at least $1300?Problem 9. How much money should you invest now in order to get $500 after 5 years at3% compounded continuously?Problem 10. A dose of 13 mg of morphine is injected into a patient’s bloodstream. Theamount of morphine in the patient’s bloodstream follows an exponential decay model witha half-life of 2.9 hours. How much morphine is in the patient’s bloodstream after 1 hour?After how much time has the amount of morphine in the patient’s bloodstream fallen to10% of the initial dose?Problem 11. A certain quantity of a radioactive substance is produced in a nuclear fissionreaction. The quantity of this substance decays over time, following an exponential decaymodel. It is found that there are 78.25 grams of this substance remaining 2 hours after thereaction, and 4 hours after the reaction there are 72.03 grams left.(a) Find the value of k in the exponential decay model for this substance. [Hint: It iseasiest to let t = 0 correspond to the point in time 2 hours after the reaction, so thatyou know the value of A0. If you do this, remember that the point in time 4 hours afterthe reaction will not be t = 4!](b) How much of this substance was originally produced in the reaction? [If in part (a) youused t = 0 to represent the point in time 2 hours after the reaction, then the first thingyou must determine is what value of t corresponds to the reaction itself.](c) What is the half-life of this substance? [This substance in this problem is supposed to bezirconium-97, so you can check your answer by searching for the half-life of zirconium-97on the Internet. The Wikipedia article “Isotopes of zirconium” is helpful.]Page 1Problem 12.(a) Convert an angle of 225◦to radians. Express your answer as a multiple of π (in otherwords, do not approximate your answer with a decimal).(b) Convert an angle of −7π12radians to degrees.Problem 13. Suppose θ is an acute angle and tan θ =158. Find the values of the otherfive trigonometric functions of θ.Problem 14. Find the exact value of (sec357◦)(sin 33◦) − tan257◦without using a calcu-lator. [Hint: Use the fundamental identities and the complementary angle theorem.]Problem 15. Find the exact value of sinπ6+ cos2π4without using a calculator.Problem 16. There is a flat field with a single large oak tree in the middle. Directly east ofthe tree, some distance away, is a white fencepost. A surveyor is standing 360 yards directlysouth of the tree. She measures the angle between her line of sight to the tree and her lineof sight to the fencepost to be 42.1◦. To the nearest yard, how far is the fencepost from thetree? How far is the surveyor from the fencepost?Here is some graph paper for you to use for something if you like.−11−11−22−22−33−33−44−44−55−55xy−11−11−22−22−33−33−44−44−55−55xyPage