JEE PYQ: Chemical Kinetics Question 31
Question 31 - 2019 (10 Apr Shift 1)
A bacterial infection in an internal wound grows as $N’(t) = N_0 \exp(t)$, where the time $t$ is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as $\frac{dN}{dt} = -5N^2$. What will be the plot of $\frac{N_0}{N}$ vs. $t$ after 1 hour?
(1) Linear with positive slope starting from origin
(2) Exponential growth
(3) Linear with positive slope starting above origin
(4) Constant
Show Answer
Answer: (3)
Solution
When drug is administered bacterial growth is given by $\frac{dN}{dt} = -5N^2$. On integrating the above equation, $\frac{N_0}{N_t} = 1 + 5tN_0$. The above equation is similar to straight line equation with positive slope. Thus $\frac{N_0}{N_t}$ increases linearly with $t$.
BETA
