Given the following function: f(x)=1.01e4x−4.62e3x−3.11e2x+12.2ex a) Use three-digit rounding frithmetic, the assumption that e1.53=4.62, and the fact that enx=(ex)n to evaluate f(1.53) b) Redo the same calculation by first rewriting the equation using the polynomial factoring technique c) Calculate the percentage relative errors in both part a) and b) to the true result f(1.53)=−7.60787

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Laith Petty · Accepted Answer

Step 1  a) f(x)=1.01e4x−4.62e3x−3.11e2x+12.2ex−1.99  f(x)=1.01(ex)4−4.62(ex)3−3.11(ex)2+12.2ex−1.99  f(1.53)=1.01(e1.53)4−4.62(e1.53)3−3.11(e1.53)2+12.2e1.53−1.99  =1.01(4.62)4−4.62(4.62)3−3.11(4.62)2+12.2(4.62)−1.99  =1.01(455.583)−4.62(98.611)−3.11(21.344)+56.364−1.99  =460.139−455.583−66.380+54.374  =−7.45  Therefore, the value of f(1.53) obtained by this method is −7.45.  Step 2  b) The given function can be factorized as follows.  f(x)=1.01(ex+1.715)(ex−0.173)(ex−1.415)(ex−4.702)  On substituting x=1.53 and using e1.53=4.62, we get  f(1.53)=1.01(4.62+1.715)(4.62−0.173)(4.62−1.415)(4.62−4.702)  =1.01(6.335)(4.447)(3.205)(−0.082)  =−7.478  Therefore, the value of f(1.53) obtained by this method is −7.478  Step 3  c) Percentage error δ is given by  δ=|VA − VEVE|  Here VA is the actual value observed and VE is the expected value which is -7.60787 in this case.  For the value obtained in part (a), the percentage error is  δa=|−7.45+7.60787−7.60787| 100%

Jeffrey Jordon · Accepted Answer

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Given the following function: f(x)=1.01e^(4x)-4.62e^(3x)-3.11e^(2x)+12.2e^(x)

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