Answer
The fractional change of the brain's volume is an increase of $3.33\times 10^{-5}$
Work Step by Step
We can find the pressure difference $\Delta P$:
$\Delta P = (31~kPa)-(101~kPa)$
$\Delta P = -70~kPa$
We can find the fraction that the volume changes:
$\frac{\Delta V}{V_0} = -\frac{1}{B}~\Delta P$
$\frac{\Delta V}{V_0} = -\left(\frac{1}{2.1\times 10^9~Pa}\right)~(-7.0\times 10^4~Pa)$
$\frac{\Delta V}{V_0} = 3.33\times 10^{-5}$
The fractional change of the brain's volume is an increase of $3.33\times 10^{-5}$.
