JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Chemical Kinetics

Bacterial growth in a culture follows first-order growth kinetics, the mirror image of radioactive decay. Radioactive decay obeys $N=N_0{e}^{-\lambda t}$, a curve that falls steeply at first and flattens as it approaches zero. Bacterial growth simply flips the sign of the exponent, $N=N_0{e}^{Kt}$ with $K>0$. This function starts at $N_0$ (never at zero, since a culture always begins with a starting population) and its slope keeps increasing with time, curving upward more and more steeply rather than levelling off. The graph that rises from $N_0$ with an increasing, concave-up (accelerating) shape represents this exponential growth.