Contagious diseases can spread very quickly. suppose five people are ill during the first week of an epidemic and that each person who is ill spreads the disease to four people by the end of the next week. by the end of the tenth week of the epidemic, how many people have been affected by the illness?

5.125 people. 
  If it takes two weeks to become sick, it means that every two weeks one person infects 4 people, 4 people infects 4 more people = 16 people are infected in week 4, 64 people in week 6, 256 people in week 8 and 1024 in week 10, multiplied by 5 initial people 5120 people, plus 5 people who inicially spread the desease =  5125 people by week 10.