Question Number 32760 by Rio Mike last updated on 01/Apr/18
$$\mathrm{if}\:{y}=\mathrm{3}{x}^{\mathrm{4}\:} .{find}\:{the}\:{approximate}\:{percentage} \\ $$$${increase}\:{in}\:{y}\:{when}\:{x}\:{increase}\:{by}\:\:\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}\%. \\ $$
Answered by MJS last updated on 02/Apr/18
$$\frac{{f}\left({x}\right)}{{f}\left({x}\right)}=\frac{\mathrm{3}\left(\mathrm{1}.\mathrm{025}{x}\right)^{\mathrm{4}} }{\mathrm{3}{x}^{\mathrm{4}} }=\mathrm{1}.\mathrm{025}^{\mathrm{4}} = \\ $$$$=\mathrm{1}.\mathrm{10318}... \\ $$$$\approx\mathrm{10}.\mathrm{32\%} \\ $$