The cumulative number of ill patients $N( t )$ during an epidemic in a country is given by the following equation $N(t)=\frac{N_0 \exp (t / \tau)}{1+N_0(\exp (t / \tau)-1) / N_s}$ where $N _0$ is the initial population of ill patients, $\tau$ a positive constant and $N _5\left( > > N _0\right)$ is a large number. Then, which of the following statements is true ?

• A

  At large time $N ( t )$ will approach zero.

• B

  The polulation curve will have an inflection point when $N ( t )$ is $N _{ s } / 2$.

• C

  $N ( t )$ will decrease monotonically.

• D

  $N( t )$ will exhibit a maximum.