{"id":12201,"date":"2015-08-17T20:52:09","date_gmt":"2015-08-17T20:52:09","guid":{"rendered":"https:\/\/courses.candelalearning.com\/osprecalc\/?post_type=chapter&p=12201"},"modified":"2019-09-09T21:31:15","modified_gmt":"2019-09-09T21:31:15","slug":"solutions-exponential-and-logarithmic-functions-practice-test","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/precalculus\/chapter\/solutions-exponential-and-logarithmic-functions-practice-test\/","title":{"raw":"Solutions: Exponential and Logarithmic Functions Practice Test","rendered":"Solutions: Exponential and Logarithmic Functions Practice Test"},"content":{"raw":"1.\u00a0About 13 dolphins.\r\n\r\n3. $1,947\r\n\r\n5.\u00a0y<\/em>-intercept: (0, 5)\r\n\"Graph\r\n\r\n7.\u00a0[latex]{8.5}^{a}=614.125[\/latex]\r\n\r\n9.\u00a0[latex]x={\\left(\\frac{1}{7}\\right)}^{2}=\\frac{1}{49}[\/latex]\r\n\r\n11.\u00a0[latex]\\mathrm{ln}\\left(0.716\\right)\\approx -0.334[\/latex]\r\n\r\n13.\u00a0Domain: x\u00a0<\/em>< 3; Vertical asymptote: x\u00a0<\/em>= 3; End behavior: [latex]x\\to {3}^{-},f\\left(x\\right)\\to -\\infty [\/latex] and [latex]x\\to -\\infty ,f\\left(x\\right)\\to \\infty [\/latex]\r\n\r\n15.\u00a0[latex]{\\mathrm{log}}_{t}\\left(12\\right)[\/latex]\r\n\r\n17.\u00a0[latex]3\\mathrm{ln}\\left(y\\right)+2\\mathrm{ln}\\left(z\\right)+\\frac{\\mathrm{ln}\\left(x - 4\\right)}{3}[\/latex]\r\n\r\n19.\u00a0[latex]x=\\frac{\\frac{\\mathrm{ln}\\left(1000\\right)}{\\mathrm{ln}\\left(16\\right)}+5}{3}\\approx 2.497[\/latex]\r\n\r\n21.\u00a0[latex]a=\\frac{\\mathrm{ln}\\left(4\\right)+8}{10}[\/latex]\r\n\r\n23.\u00a0no solution\r\n\r\n25.\u00a0[latex]x=\\mathrm{ln}\\left(9\\right)[\/latex]\r\n\r\n27.\u00a0[latex]x=\\pm \\frac{3\\sqrt{3}}{2}[\/latex]\r\n\r\n29.\u00a0[latex]f\\left(t\\right)=112{e}^{-.019792t}[\/latex]; half-life: about 35 days\r\n\r\n31.\u00a0[latex]T\\left(t\\right)=36{e}^{-0.025131t}+35;T\\left(60\\right)\\approx {43}^{\\text{o}}\\text{F}[\/latex]\r\n\r\n33. logarithmic\r\n\"Graph\r\n\r\n35.\u00a0exponential; [latex]y=15.10062{\\left(1.24621\\right)}^{x}[\/latex]\r\n\"Graph\r\n\r\n37.\u00a0logistic; [latex]y=\\frac{18.41659}{1+7.54644{e}^{-0.68375x}}[\/latex]\r\n\"Graph","rendered":"

1.\u00a0About 13 dolphins.<\/p>\n

3. $1,947<\/p>\n

5.\u00a0y<\/em>-intercept: (0, 5)
\n\"Graph<\/p>\n

7.\u00a0[latex]{8.5}^{a}=614.125[\/latex]<\/p>\n

9.\u00a0[latex]x={\\left(\\frac{1}{7}\\right)}^{2}=\\frac{1}{49}[\/latex]<\/p>\n

11.\u00a0[latex]\\mathrm{ln}\\left(0.716\\right)\\approx -0.334[\/latex]<\/p>\n

13.\u00a0Domain: x\u00a0<\/em>< 3; Vertical asymptote: x\u00a0<\/em>= 3; End behavior: [latex]x\\to {3}^{-},f\\left(x\\right)\\to -\\infty[\/latex] and [latex]x\\to -\\infty ,f\\left(x\\right)\\to \\infty[\/latex]<\/p>\n

15.\u00a0[latex]{\\mathrm{log}}_{t}\\left(12\\right)[\/latex]<\/p>\n

17.\u00a0[latex]3\\mathrm{ln}\\left(y\\right)+2\\mathrm{ln}\\left(z\\right)+\\frac{\\mathrm{ln}\\left(x - 4\\right)}{3}[\/latex]<\/p>\n

19.\u00a0[latex]x=\\frac{\\frac{\\mathrm{ln}\\left(1000\\right)}{\\mathrm{ln}\\left(16\\right)}+5}{3}\\approx 2.497[\/latex]<\/p>\n

21.\u00a0[latex]a=\\frac{\\mathrm{ln}\\left(4\\right)+8}{10}[\/latex]<\/p>\n

23.\u00a0no solution<\/p>\n

25.\u00a0[latex]x=\\mathrm{ln}\\left(9\\right)[\/latex]<\/p>\n

27.\u00a0[latex]x=\\pm \\frac{3\\sqrt{3}}{2}[\/latex]<\/p>\n

29.\u00a0[latex]f\\left(t\\right)=112{e}^{-.019792t}[\/latex]; half-life: about 35 days<\/p>\n

31.\u00a0[latex]T\\left(t\\right)=36{e}^{-0.025131t}+35;T\\left(60\\right)\\approx {43}^{\\text{o}}\\text{F}[\/latex]<\/p>\n

33. logarithmic
\n\"Graph<\/p>\n

35.\u00a0exponential; [latex]y=15.10062{\\left(1.24621\\right)}^{x}[\/latex]
\n\"Graph<\/p>\n

37.\u00a0logistic; [latex]y=\\frac{18.41659}{1+7.54644{e}^{-0.68375x}}[\/latex]
\n\"Graph<\/p>\n\n\t\t\t

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