Elijah has some good news to share. He sends an e-mail to 3 of his friends (call this round 1). Each of these friends forwards the e-mail to 3 other people (round 2). Those 9 people each forward the e-mail to 3 other people (round 3), and so on. Assume that nobody receives the e-mail more than once.
a. Determine an expression for the number of people who receive an e-mail in the nth round.
b. Determine an expression for the total number of people, including Elijah, who are aware of the good news by the nth round.
c. Calculate the number of people who receive the e-mail in the 6th round.
d. Calculate the total number of people, including Elijah, who are aware of the good news by the 6th round.