Question

y^2 is directly proportional to x^3. If y is doubles find the percentage increase in x

Answer 1

\[y^2=kx^3\]
for some real \(k\).

When \(y\) doubles:
\[(2y)^2=4y^2=4kx^3=k\left(4^{1/3}x\right)^3\approx k(1.587x)^3\]
The percentage increase is approximately 59%, because \(1.59x=x+\color{red}{.59x}\).