Question: Chain Letters

Suppose you receive a chain letter asking you to send $1 to the person at the top of the list of six names, then to add your name to the bottom of the list, and finally to send the revised letter to six people. The promise is that when the letters have been sent to each of the people above you on the list, you will be at the top of the list and you will receive a large amount of money. To investigate whether this is worth the dollar that you are asked to spend, create the requested models and answer the following questions.

a) Suppose each of the six persons on the original list sent six letters. How much money would the person on the top of the list receive?

b) Consider the person who is second on the original list. How much money would this person receive?

c) Complete the partial table of amounts that will be sent to the person on the top of the list during each “cycle” of the chain letter.

d) If you were going to start such a chain letter, would you put your name at the top of the fist six names or as number 5?

e) Find the best quadratic, power, and exponential models for the data in the table. Which of these function types gives the best model for the data?

f) Use the exponential function found in part (5) to determine the amount of money the person who was at the bottom of the original list would receive if all people contacted send the $1 and mail the letter to 6 additional people.

g) How many people will have to respond to the chain letter for the sixth person on the original list to receive all the money that was promised?

h) If you receive that letter in its tenth cycle, how many other people have been contacted, along with you, assuming that everyone who receives the letter cooperates with its suggestions?

I ) Who remains in the U.S. for you to send your letter to, if no one sends a letter to someone who has already received it?