Growth rate in number of days of number of active cases is given as $2 = x^{14}$
$\implies x = 2^{1/14}$
Current number of active cases is $20,000$ and we need $100,000$ for the hospital beds to run out.
So, number of days $d$ within which hospital beds will run out is given by
$100,000 \leq 20,000 \times x^d$
$\implies 5 \leq \left(2^{1/14}\right)^d$
$\implies 5 \leq 2^{d/14}$
$\implies d \geq 14 \times \log_2 5 = 14 \times 2.32 = 32.48$
So, on the $33^{rd}$ day the hospital beds will run out.
Correct answer : D