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

Bevan Mcdonald 2020-10-19 Answered

Given the following function:
f(x)=1.01e4x4.62e3x3.11e2x+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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Expert Answer

Laith Petty
Answered 2020-10-20 Author has 103 answers
Step 1
a) f(x)=1.01e4x4.62e3x3.11e2x+12.2ex1.99
f(x)=1.01(ex)44.62(ex)33.11(ex)2+12.2ex1.99
f(1.53)=1.01(e1.53)44.62(e1.53)33.11(e1.53)2+12.2e1.531.99
=1.01(4.62)44.62(4.62)33.11(4.62)2+12.2(4.62)1.99
=1.01(455.583)4.62(98.611)3.11(21.344)+56.3641.99
=460.139455.58366.380+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)(ex0.173)(ex1.415)(ex4.702)
On substituting x=1.53 and using e1.53=4.62, we get
f(1.53)=1.01(4.62+1.715)(4.620.173)(4.621.415)(4.624.702)
=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+7.607877.60787| 100%
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Jeffrey Jordon
Answered 2022-01-15 Author has 2087 answers

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