When a zombie virus outbreak begins, the number of people who are infected increases slowly at first. As the virus spreads, the rate of increase gets greater, and then when most of the population are zombies the rate of increase slows.
Consider \( z=f(t) \) , where \(z\) is the number of zombies, and \( t \) is time.

a) The function is increasing because as the virus spreads there will be more and more zombies. Eventually there will be no one left to infect and the function will become more or less constant.
b) During the early phase, as the rate of infection increases, the function will be concave up, but as the number of uninfected shrinks and the infection rate drops, the function will become concave down.