Answer
$\approx 2.92$ sec.
Work Step by Step
If t varies inversely with $A^{2}$, then $t=\displaystyle \frac{k}{A^{2}}$, for some constant k.
Given $t=3.4$ when $A=0.089,$
$ 3.4=\displaystyle \frac{k}{(0.089)^{2}}\qquad$... multiply with $(0.089)^{2}$
$3.4(0.089)^{2}=k$
$k=0.0269314$
For A=0.096,
$t=\displaystyle \frac{0.0269314}{(0.096)^{2}}\approx 2.92$ sec.
