Question

the senior class advisor sends an e - mail to 7 students. that day, each student who receives the e - mail sends it to two friends. each friend who receives the e - mail sends it to two more friends the following day. consider an expression used to determine the number of people who receive the e - mail on day n, if the pattern continues. parts of the expression are shown. interpret the meaning of each part and match it to the expression. 2 7 $7(2)^{n}$ initial number of people who receive the e - mail the increasing factor

Explanation:

• The value 2 represents how each recipient shares the email: every person who gets the email sends it to 2 new people, so this is the increasing factor for the chain.
• The value 7 is the first group of people to receive the email, sent directly by the advisor, so this is the initial number of email recipients.
• The expression $7(2)^n$ combines the initial number and the increasing factor to calculate the total number of people who receive the email on day $n$.

Answer:

• $2$ → The increasing factor
• $7$ → Initial number of people who receive the e-mail
• $7(2)^n$ → Total number of people who receive the e-mail on day $n$