Answer
Increase by a factor of $10$
Work Step by Step
We are given the model: $pH=2$
$[p H]=-\log [H^{+}] \implies 2=-\log [H^{+}]_{initial}$
$[H^{+}]_{initial}= 0.01$
$[H^{+}]_{after}= 0.1$
$\dfrac{[H^{+}]_{initial}}{[H^{+}]_{after}} =\dfrac{0.1}{0.01}$
$=10$
Our answer is: Increase by a factor of $10$.