# MATH107Quiz5SOLNS.pdf - MATH 107 QUIZ 5 SOLUTIONS October,...

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MATH 107 QUIZ 5 SOLUTIONSOctober, 2018Instructor: S. Sands1. (4 pts) Which of these graphs represent a one-to-one function?Answer(s):A(no explanation required.)(There may be more than one graph that qualifies.)(A)No vertical or horizontal linecrosses the graph more thanonce, so the graph representsa function, and also is a one-to-one function.(B)Not a function (verticalline crosses graph morethan once), so not a one-to-one function.(C)The horizontal liney=3intersects the graph more thanonce(D)There are horizontallines crossing the graphmore than once.2. (6 pts) Based on data about the growth of a particular species of trees, the following logarithmic modelabout these trees was determined:h(t) = 6.2(ln(t) + 1),wheret= age of tree in years andh(t) = height of tree, in feet.(Note that "ln" refers to the natural log function)(explanation optional)Using the model,(a) At age 5 years, how tall is this type of tree, to the nearest tenth of a foot?h(5) = 6.2 ( ln(5) + 1)6.2 (2.6094)16.2The model estimates that the 5-year-old tree will be 16.2 feet tall.(b) At age 20 years, how tall is this type of tree, to the nearest tenth of a foot?h(20) = 6.2 ( ln(20) + 1)6.2 (3.9957)24.8The model estimates that the 20-year-old tree will be 24.8 feet tall.3. (4 pts)Convert to a logarithmic equation: 8x= 128.(no explanation required)3.CA.log?128 = 8B.log8? = 128C.𝐥𝐨𝐠𝟖??𝟖 = 𝒙The base is 8. The value of the log is the exponentx.D.log?8 = 128
4.(8 pts)Solve the equation.Checkall proposed solutions.Show work in solving and in checking, and state yourfinal conclusion.[section 0.9, 5.3]√44 − ?= 2 − ?(√44 − ?)2= (2 − ?)2Square both sides.44x= 44x+x20 =x23x400 = (x8)(x+ 5)x8 = 0 orx+ 5 = 0x= 8 orx=5.Potential solutionsCheck:x= 8:x=5:√44 − 8? 2 − 8√44 − (−5)? 2 − (−5)√36? −6√49? 76 ≠ −67 = 7The equation is NOT satisfied.x= 8is NOT a solution.x=5IS a solution.x=5 is theonlysolution.5. (8 pts)(a)log31 = 0because 30= 1. For any baseb,log1b= 0.(b)Let? = log31√3State the exponential form of the equation.?𝒙=1√3(c)Determine the numerical value oflog31√3in simplest form. Work optional.Since1√3=131/2= 3−1/2, we have3?= 3−1/2We raise 3 to the1/2power in order to get1√3.x=1/2,so? = log31√3= −??Alternatively,log31√3= log31 − log3√3= 0 − log3312= −12log33 = −12(1) = −?

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