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…

A bacterial infection in an internal wound grows as $\displaystyle \mathrm{N}^{\prime}(\mathrm{t})=\mathrm{N}_0 \exp (\mathrm{t})$, where the time t is in hours. A dose of antibiotic, taken orally, needs $\displaystyle 1$ hour to reach the wound. Once it reaches there, the bacterial population goes down as $\displaystyle \frac{d N}{d t}=-5 N^2$. What will be the plot of $\displaystyle \frac{\mathrm{N}_0}{\mathrm{~N}}$ vs. t after $\displaystyle 1$ hour ?