Suppose That an Epidemic Is Spreading at a Rate Proportional $y ^ { \prime } = g ( y )$

Suppose that an epidemic is spreading at a rate proportional to the square of the infected population. Let f(t) be the number of infected people at time t, and suppose y = f(t) satisfies a differential equation $y ^ { \prime } = g ( y )$ . Which of the following sets of curves could represent solutions of $y ^ { \prime } = g ( y ) ?$ [Hint: First determine the differential equation $y ^ { \prime }$ = g(y) .]

A)
B)
C)
D)