Question

If $y$ varies inversely with the fourth root of x, and $y=4$ when $x=\frac{1}{16}$, then what is the value of $y$ when $x=\frac{1}{81}$ ?

Answer 1

Let the Function representing above condition be

$y=\frac{c}{x^{1/4}}\Rightarrow 4=\frac{c}{(\frac{1}{16}{)}^{1/4}}\Rightarrow 4=2c\Rightarrow c=2$

$y=\frac{2}{(\frac{1}{81}{)}^{1/4}}=\frac{2}{\frac{1}{3}}=6$