$A$ swimming pool has a depth of $22 \ m$ and area $700 \ m^2$. Calculate the fractional change $\frac{\Delta V}{V}$ of water at the bottom of the swimming pool. Given that the bulk modulus of water is $2.2 \times 10^9 \ N \ m^{-2}$, $g = 10 \ m \ s^{-2}$, and the density of water is $1000 \ kg \ m^{-3}$.

• A
  $2.2 \times 10^{-4}$
• B
  $0.7 \times 10^{-4}$
• C
  $0.31 \times 10^{-4}$
• D
  $10^{-4}$