Solution
= Solution
Per unit depth, the bubble volume is its area $V=\pi a^2$. At equilibrium its pressure equals $p_\infty$, so $p_0V=p_\infty\pi a_0^2$. Hence
$$
p_0=p_\infty\frac{a_0^2}{a^2}
=p_\infty(1+\epsilon)^{-2}
=p_\infty(1-2\epsilon)+O(\epsilon^2).
$$
Continuity of <fluid pressure> at the interface gives $p(a,t)=p_0(t)$. Consequently
$$
\boxed{p(a,t)-p_\infty=-2p_\infty\epsilon+O(\epsilon^2)}.
$$