# GATE2018-44

Moist heat sterilization of spores at $121 ^\circ C$ follows first order kinetics as per the expression: $$\dfrac{dN}{dt}=-k_dN$$ where, $N$ is the number of viable spores, $t$I is the time, $k_d$ is the rate constant and $\dfrac{dN}{dt}$ is the rate of change of viable spores.
If $k_d$ value is $1.0 \text{min}^{-1}$, the time (in minutes) required to reduce the number of viable spores from an initial value of $10^{10}$ to a final value of $1$ is (up to two decimal places) __________