Answer
increases by $4$ times
Work Step by Step
The variation model described by the problem is $
y=kx^2
.$
If $x=1,$ then
\begin{array}{l}\require{cancel}
y_1=k(1)^2
\\
y_1=k(1)
\\
y_1=k
.\end{array}
If $x=2$ ($x$ is doubled), then
\begin{array}{l}\require{cancel}
y_2=k(2)^2
\\
y_2=k(4)
\\
y_2=4k
.\end{array}
Comparing $y_1$ and $y_2$, when $x$ is doubled, then $y$ increases by $4$ times.
