{"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":"2015-11-12T18:37:58","modified_gmt":"2015-11-12T18:37:58","slug":"solutions-54","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/chapter\/solutions-54\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"

Solutions to Try Its<\/span><\/h2>\n1.\u00a0[latex]\\frac{$2.84-$2.31}{5\\text{ years}}=\\frac{$0.53}{5\\text{ years}}=$0.106[\/latex] per year.\n\n2.\u00a0[latex]\\frac{1}{2}\\\\[\/latex]\n\n3.\u00a0[latex]a+7\\\\[\/latex]\n\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].\n\n\n\"Graph<\/span>\n

Solution to Odd-Numbered Exercises<\/span><\/h2>\n1.\u00a0Yes, the average rate of change of all linear functions is constant.\n\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.\n\n5.\u00a0[latex]4\\left(b+1\\right)\\\\[\/latex]\n\n7. 3\n\n9.\u00a0[latex]4x+2h[\/latex]\n\n11.\u00a0[latex]\\frac{-1}{13\\left(13+h\\right)}\\\\[\/latex]\n\n13.\u00a0[latex]3{h}^{2}+9h+9\\\\[\/latex]\n\n15.\u00a0[latex]4x+2h - 3\\\\[\/latex]\n\n17.\u00a0[latex]\\frac{4}{3}\\\\[\/latex]\n\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]\n\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]\n\n23. local maximum: [latex]\\left(-3,\\text{ }60\\right)\\\\[\/latex], local minimum: [latex]\\left(3,\\text{ }-60\\right)\\\\[\/latex]\n\n25.\u00a0absolute maximum at approximately [latex]\\left(7,\\text{ }150\\right)\\\\[\/latex], absolute minimum at approximately [latex]\\left(-7.5,\\text{ }-220\\right)\\\\[\/latex]\n\n27.\u00a0a. \u20133000; b. \u20131250\n\n29. \u20134\n\n31. 27\n\n33.\u00a0\u20130.167\n\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]\n\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]\n\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]\n\n41. A)\u00a0a relative (local) maximum of the function\n\n43.\u00a0[latex]b=5[\/latex]\n\n45.\u00a02.7 gallons per minute\n\n47.\u00a0approximately \u20130.6 milligrams per day\n\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

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