When a rumor begins, the number of people who have heard the rumor increases slowly at first. As the rumor spreads, the rate of increase gets greater (as more people continue to tell their friends the rumor), and then slows down again (when almost everyone has heard the rumor). Let denote the number of people who have heard the rumor hours after the rumor has begun.

(a) Based on this description, the function is




(b) Based on this description, the graph of the function will be




You can earn partial credit on this problem.