"Pay it Forward" Exponential Growth Activity (Learn by Doing - Preview of up coming content) The story: Young Trevor, is caught up by an intriguing assignment from his new social studies teacher, Mr. Simonet. The assignment: think of something to change the world and put it into action. Trevor conjures the notion of paying a favor not back, but forward--repaying good deeds not with payback, but with new good deeds done to three new people. Trevor's efforts to make good on his idea bring a revolution not only in the lives of himself, his mother and his teacher, but in those of an ever-widening circle of people completely unknown to him. First you need make some assumptions: How Long does each person get to complete the 3 good deeds? (1 day, 1 week, 1 month...) Once someone has a good deed done to them they do not receive another good deed until after everyone else receives one. Now complete the table for at least seven rounds of good deeds and see if you can find an equation to fit the growth process. Time in: Number of New Total People People Helped Helped Start (0) 1 3 4 2 9 13 3 27 40 4 1 21 5 243 364 729 1093 7 2187 32 80 8 6581 98601 9 19 483 29544 16 59049 88 593 1 1 177147 2 6 5740 12 531 441 797181 nQuestions to consider once you have found and tested your mathematical model... 1. How many new people would be helped during the 12th round of good deeds? What is the total number of people who have been helped by the end of the 12th round? new people helped: 53141 Total people helped : 797 181 2. There are about 4.7 million people in the Metro Phoenix area, how long would it take for everyone in the Phoenix Metropolitan area to receive a good deed? (Census Bureau 2017) 3. There are about 7.3 million people in Arizona, how long would it take for everyone in Arizona to receive a good deed? (Census Bureau 2019) 4. There are about 328.2 million people in the USA, how long would it take for everyone in the USA to receive a good deed? (Census Bureau 2019) 5. There are 7.7 billion people in the world, how long before everyone in the world would receive a good deed? 6. What do the numbers tell you about the possibility of changing the world for the better? 7. What is needed to make it happen