A person's wound was exposed to some bacteria and then bacteria growth started to happen at the same place. Th…

Question

A person's wound was exposed to some bacteria and then bacteria growth started to happen at the same place. The wound was later treated with some antibacterial medicine and the rate of bacterial decay ( $r$ ) was found to be proportional with the square of the existing number of bacteria at any instance. Which of the following set of graphs correctly represents the 'before' and 'after' situation of the application of the medicine?

[Given: $N$ = No. of bacteria, $t$ = time, bacterial growth follows $1$ st order kinetics.]

Four options of paired graphs labeled Before and After, comparing bacterial growth versus time and decay rate versus number of bacteria.

[Given: $$N$$ = No. of bacteria, $$t$$ = time, bacterial growth follows $$1$$st order kinetics.]

Accepted Answer

B. **(2)** *Before*: $$\frac{N}{N_0}$$ rises exponentially from $$1$$ as $$t$$ increases. *After*: $$r$$ rises from the origin along an upward-curving (parabolic) graph as $$N$$ increases.

Answer

A. **(1)** *Before*: $$\frac{N}{N_0}$$ rises exponentially from $$1$$ as $$t$$ increases. *After*: $$r$$ starts high and falls off as $$N$$ increases.

Answer

C. **(3)** *Before*: $$\frac{N}{N_0}$$ rises from $$0$$ rather than from $$1$$ at $$t = 0$$. *After*: $$r$$ rises from the origin along an upward-curving graph as $$N$$ increases.

Answer

D. **(4)** *Before*: $$\frac{N}{N_0}$$ rises exponentially from $$1$$ as $$t$$ increases. *After*: $$r$$ increases linearly with $$N$$.

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