A person's wound was exposed to some bacteria and then bacterial 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 1st order kinetics.]
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Answer
(3) [figure]
Solution
Before the medicine (first-order growth):
dNdt = kN N = N0ekt NN0 = ekt
At t = 0, NN0 = 1, and it then rises exponentially (curving upward).
The 'Before' graph starts at 1 on the NN0 axis — true for (1), (3) and (4), not for (2) (starts at 0).
After the medicine:
r = k'N2 r = 0 at N = 0 and r increases as a parabola (curving upward) with N.
(1) (straight line) and (4) (decreasing curve) are wrong; (3) shows the parabola.
Answer: (3)