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]](Q39171.png)
$${Given}\:{that}\: \\ $$$${y}\:=\:\mathrm{3}{x}^{\mathrm{4}} \:{and}\:{x}\:{increases} \\ $$$${at}\:{the}\:{rate}\:{of}\:\mathrm{34\%}\:. \\ $$$${find}\:{the}\:{percentage}\:{increase} \\ $$$${in}\:{y}. \\ $$$$\left[{hint}:\:{using}\:{Bionomial}\:\right. \\ $$$$\left.{method}\right] \\ $$
Answered by MrW3 last updated on 03/Jul/18
$${y}\left(\mathrm{1}+\beta\right)=\mathrm{3}{x}^{\mathrm{4}} \left(\mathrm{1}+\alpha\right)^{\mathrm{4}} \\ $$$$\beta=\left(\mathrm{1}+\alpha\right)^{\mathrm{4}} −\mathrm{1}=\mathrm{4}\alpha+\mathrm{6}\alpha^{\mathrm{2}} +\mathrm{4}\alpha^{\mathrm{3}} +\alpha^{\mathrm{4}} \\ $$$${with}\:\alpha=\mathrm{0}.\mathrm{34} \\ $$$$\Rightarrow\beta=\mathrm{2}.\mathrm{22}=\mathrm{222\%} \\ $$