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Given-that-y-3x-4-and-x-increases-at-the-rate-of-34-find-the-percentage-increase-in-y-hint-using-Bionomial-method-




Question Number 39171 by Rio Mike last updated on 03/Jul/18
Given that   y = 3x^4  and x increases  at the rate of 34% .  find the percentage increase  in y.  [hint: using Bionomial   method]
$${Given}\:{that}\: \\ $$$${y}\:=\:\mathrm{3}{x}^{\mathrm{4}} \:{and}\:{x}\:{increases} \\ $$$${at}\:{the}\:{rate}\:{of}\:\mathrm{34\%}\:. \\ $$$${find}\:{the}\:{percentage}\:{increase} \\ $$$${in}\:{y}. \\ $$$$\left[{hint}:\:{using}\:{Bionomial}\:\right. \\ $$$$\left.{method}\right] \\ $$
Answered by MrW3 last updated on 03/Jul/18
y(1+β)=3x^4 (1+α)^4   β=(1+α)^4 −1=4α+6α^2 +4α^3 +α^4   with α=0.34  ⇒β=2.22=222%
$${y}\left(\mathrm{1}+\beta\right)=\mathrm{3}{x}^{\mathrm{4}} \left(\mathrm{1}+\alpha\right)^{\mathrm{4}} \\ $$$$\beta=\left(\mathrm{1}+\alpha\right)^{\mathrm{4}} −\mathrm{1}=\mathrm{4}\alpha+\mathrm{6}\alpha^{\mathrm{2}} +\mathrm{4}\alpha^{\mathrm{3}} +\alpha^{\mathrm{4}} \\ $$$${with}\:\alpha=\mathrm{0}.\mathrm{34} \\ $$$$\Rightarrow\beta=\mathrm{2}.\mathrm{22}=\mathrm{222\%} \\ $$

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