{"id":900,"date":"2015-11-12T18:37:58","date_gmt":"2015-11-12T18:37:58","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=900"},"modified":"2017-03-31T20:14:37","modified_gmt":"2017-03-31T20:14:37","slug":"solutions-54","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/solutions-54\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"

Solutions to Try Its<\/span><\/h2>\r\n1.\u00a0[latex]\\frac{$2.84-$2.31}{5\\text{ years}}=\\frac{$0.53}{5\\text{ years}}=$0.106[\/latex] per year.\r\n\r\n2.\u00a0[latex]\\frac{1}{2}[\/latex]\r\n\r\n3.\u00a0[latex]a+7[\/latex]\r\n\r\n4.\u00a0The local maximum appears to occur at [latex]\\left(-1,28\\right)[\/latex], and the local minimum occurs at [latex]\\left(5,-80\\right)[\/latex]. The function is increasing on [latex]\\left(-\\infty ,-1\\right)\\cup \\left(5,\\infty \\right)[\/latex] and decreasing on [latex]\\left(-1,5\\right)[\/latex].\r\n\r\n\r\n\"Graph<\/span>\r\n

Solution to Odd-Numbered Exercises<\/span><\/h2>\r\n1.\u00a0Yes, the average rate of change of all linear functions is constant.\r\n\r\n3.\u00a0The absolute maximum and minimum relate to the entire graph, whereas the local extrema relate only to a specific region around an open interval.\r\n\r\n5.\u00a0[latex]4\\left(b+1\\right)[\/latex]\r\n\r\n7. 3\r\n\r\n9.\u00a0[latex]4x+2h[\/latex]\r\n\r\n11.\u00a0[latex]\\frac{-1}{13\\left(13+h\\right)}[\/latex]\r\n\r\n13.\u00a0[latex]3{h}^{2}+9h+9[\/latex]\r\n\r\n15.\u00a0[latex]4x+2h - 3[\/latex]\r\n\r\n17.\u00a0[latex]\\frac{4}{3}[\/latex]\r\n\r\n19.\u00a0increasing on [latex]\\left(-\\infty ,-2.5\\right)\\cup \\left(1,\\infty \\right)[\/latex], decreasing on [latex]\\left(-2.5,\\text{ }1\\right)[\/latex]\r\n\r\n21.\u00a0increasing on [latex]\\left(-\\infty ,1\\right)\\cup \\left(3,4\\right)[\/latex], decreasing on [latex]\\left(1,3\\right)\\cup \\left(4,\\infty \\right)[\/latex]\r\n\r\n23. local maximum: [latex]\\left(-3,\\text{ }60\\right)[\/latex], local minimum: [latex]\\left(3,\\text{ }-60\\right)[\/latex]\r\n\r\n25.\u00a0absolute maximum at approximately [latex]\\left(7,\\text{ }150\\right)[\/latex], absolute minimum at approximately [latex]\\left(-7.5,\\text{ }-220\\right)[\/latex]\r\n\r\n27.\u00a0a. \u20133000; b. \u20131250\r\n\r\n29. \u20134\r\n\r\n31. 27\r\n\r\n33.\u00a0\u20130.167\r\n\r\n35.\u00a0Local minimum at [latex]\\left(3,-22\\right)[\/latex], decreasing on [latex]\\left(-\\infty ,\\text{ }3\\right)[\/latex], increasing on [latex]\\left(3,\\text{ }\\infty \\right)[\/latex]\r\n\r\n37.\u00a0Local minimum at [latex]\\left(-2,-2\\right)[\/latex], decreasing on [latex]\\left(-3,-2\\right)[\/latex], increasing on [latex]\\left(-2,\\text{ }\\infty \\right)[\/latex]\r\n\r\n39.\u00a0Local maximum at [latex]\\left(-0.5,\\text{ }6\\right)[\/latex], local minima at [latex]\\left(-3.25,-47\\right)[\/latex] and [latex]\\left(2.1,-32\\right)[\/latex], decreasing on [latex]\\left(-\\infty ,-3.25\\right)[\/latex] and [latex]\\left(-0.5,\\text{ }2.1\\right)[\/latex], increasing on [latex]\\left(-3.25,\\text{ }-0.5\\right)[\/latex] and [latex]\\left(2.1,\\text{ }\\infty \\right)[\/latex]\r\n\r\n41. A)\u00a0a relative (local) maximum of the function\r\n\r\n43.\u00a0[latex]b=5[\/latex]\r\n\r\n45.\u00a02.7 gallons per minute\r\n\r\n47.\u00a0approximately \u20130.6 milligrams per day\r\n\r\n\u00a0","rendered":"

Solutions to Try Its<\/span><\/h2>\n

1.\u00a0[latex]\\frac{$2.84-$2.31}{5\\text{ years}}=\\frac{$0.53}{5\\text{ years}}=$0.106[\/latex] per year.<\/p>\n

2.\u00a0[latex]\\frac{1}{2}[\/latex]<\/p>\n

3.\u00a0[latex]a+7[\/latex]<\/p>\n

4.\u00a0The local maximum appears to occur at [latex]\\left(-1,28\\right)[\/latex], and the local minimum occurs at [latex]\\left(5,-80\\right)[\/latex]. The function is increasing on [latex]\\left(-\\infty ,-1\\right)\\cup \\left(5,\\infty \\right)[\/latex] and decreasing on [latex]\\left(-1,5\\right)[\/latex].<\/p>\n


\n\"Graph<\/span><\/p>\n

Solution to Odd-Numbered Exercises<\/span><\/h2>\n

1.\u00a0Yes, the average rate of change of all linear functions is constant.<\/p>\n

3.\u00a0The absolute maximum and minimum relate to the entire graph, whereas the local extrema relate only to a specific region around an open interval.<\/p>\n

5.\u00a0[latex]4\\left(b+1\\right)[\/latex]<\/p>\n

7. 3<\/p>\n

9.\u00a0[latex]4x+2h[\/latex]<\/p>\n

11.\u00a0[latex]\\frac{-1}{13\\left(13+h\\right)}[\/latex]<\/p>\n

13.\u00a0[latex]3{h}^{2}+9h+9[\/latex]<\/p>\n

15.\u00a0[latex]4x+2h - 3[\/latex]<\/p>\n

17.\u00a0[latex]\\frac{4}{3}[\/latex]<\/p>\n

19.\u00a0increasing on [latex]\\left(-\\infty ,-2.5\\right)\\cup \\left(1,\\infty \\right)[\/latex], decreasing on [latex]\\left(-2.5,\\text{ }1\\right)[\/latex]<\/p>\n

21.\u00a0increasing on [latex]\\left(-\\infty ,1\\right)\\cup \\left(3,4\\right)[\/latex], decreasing on [latex]\\left(1,3\\right)\\cup \\left(4,\\infty \\right)[\/latex]<\/p>\n

23. local maximum: [latex]\\left(-3,\\text{ }60\\right)[\/latex], local minimum: [latex]\\left(3,\\text{ }-60\\right)[\/latex]<\/p>\n

25.\u00a0absolute maximum at approximately [latex]\\left(7,\\text{ }150\\right)[\/latex], absolute minimum at approximately [latex]\\left(-7.5,\\text{ }-220\\right)[\/latex]<\/p>\n

27.\u00a0a. \u20133000; b. \u20131250<\/p>\n

29. \u20134<\/p>\n

31. 27<\/p>\n

33.\u00a0\u20130.167<\/p>\n

35.\u00a0Local minimum at [latex]\\left(3,-22\\right)[\/latex], decreasing on [latex]\\left(-\\infty ,\\text{ }3\\right)[\/latex], increasing on [latex]\\left(3,\\text{ }\\infty \\right)[\/latex]<\/p>\n

37.\u00a0Local minimum at [latex]\\left(-2,-2\\right)[\/latex], decreasing on [latex]\\left(-3,-2\\right)[\/latex], increasing on [latex]\\left(-2,\\text{ }\\infty \\right)[\/latex]<\/p>\n

39.\u00a0Local maximum at [latex]\\left(-0.5,\\text{ }6\\right)[\/latex], local minima at [latex]\\left(-3.25,-47\\right)[\/latex] and [latex]\\left(2.1,-32\\right)[\/latex], decreasing on [latex]\\left(-\\infty ,-3.25\\right)[\/latex] and [latex]\\left(-0.5,\\text{ }2.1\\right)[\/latex], increasing on [latex]\\left(-3.25,\\text{ }-0.5\\right)[\/latex] and [latex]\\left(2.1,\\text{ }\\infty \\right)[\/latex]<\/p>\n

41. A)\u00a0a relative (local) maximum of the function<\/p>\n

43.\u00a0[latex]b=5[\/latex]<\/p>\n

45.\u00a02.7 gallons per minute<\/p>\n

47.\u00a0approximately \u20130.6 milligrams per day<\/p>\n

\u00a0<\/p>\n\n\t\t\t

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