Math 1051, Summer 2007, Exam IIIName:Instructions: This is the third midterm exam for Math 1051, precalculus.You have 55 minutes to complete the test. Do not start until you are told tobegin.When you receive this bo oklet, count the pages to be sure that you have everypage. There should be 6 pages, including this cover sheet. When you aretold to begin, be sure to put your name on every page of the exam booklet,in case pages become separated in the grading process.No notes or books are allowed on this exam. Scientific calculators are allowed,however, calculators with graphing capabilities may not be used. You shouldsimplify all fractions when they appear in your answer.There are a total of 80 points, distributed among 9 problems. T he problemsare worth varying amounts. You must show your work for all problems.Little or no credit will be given for unsupported answers. Even if you cando the problems in your head, you must c onvince me that you know whatyou’re doing. Good luck.Problem Points Possible1 82 103 104 65 106 127 68 109 8Total 8011. (8 points) Let f(x) = ex+1. Determine f−1(x), and verify that f (f−1(x)) =x.2. (10 points) Simplify as much as possible:log((101000− 1)(101000+ 1) + 1).23. (10 points) $5,000 is invested at 10% interest compounded continuously.(a) Find the doubling time to the nearest hundredth of a year.(b) Find out, to the nearest tenth of a year, how long it will take for the$5,000 to grow to $40,0004. (6 points) What is the slope of all lines that are perpendicular to theline7x − 2y = 9?35. (10 points) The radioactive isotope sodium-24 is used as a tracer tomeasure the rate of flow in an artery or vein. The half-life of sodium-24 is14.9 hours. Suppose that a hospital buys a 40 gram sample of sodium-24.(a) How much of the sample will remain after 44.7 hours? (Express youranswer to the nearest tenth of a gram)(b) How long will it be until only 1.25 grams remain? (Express youranswer to the nearest tenth of an hour)46. (12 points) Create a table and graph the equationf(x) =4x2.Determine the domain and range.7. (6 points) Let f (x) =√x − 2 and g(x) = x2+ 4x. Determine f(g(x))and g(f(x)).58. (10 points) The number of days needed to assemble some machines variesdirectly as the number of machines and inversely as the number of peopleworking. If it takes 4 people 32 days to assemble 16 machines, how manydays will it take 16 people to assemble 48 machines?9. (8 points) Create a table and graph x+1 = |y|. Is this a function (justifyyour