a young entrepreneur is starting a new company and decides to send a promotional email offering a free…

a young entrepreneur is starting a new company and decides to send a promotional email offering a free sample of his product to anyone who receives the email. his plan is to send the promotional email to 15 contacts with a request to forward the email to four different people. suppose that the young entrepreneur sends the email to 15 contacts on day 1. on day 2, each recipient sends the email to 4 different people. on day 3, each of the new recipients sends the email to 4 different people. if the process continues, how many emails will be sent on day ten? 91,125 3mails 983,040 emails 15,728,640 10,125 emails 3,932,160 emails

a young entrepreneur is starting a new company and decides to send a promotional email offering a free sample of his product to anyone who receives the email. his plan is to send the promotional email to 15 contacts with a request to forward the email to four different people. suppose that the young entrepreneur sends the email to 15 contacts on day 1. on day 2, each recipient sends the email to 4 different people. on day 3, each of the new recipients sends the email to 4 different people. if the process continues, how many emails will be sent on day ten? 91,125 3mails 983,040 emails 15,728,640 10,125 emails 3,932,160 emails

Answer

Answer:

C. 15,728,640

Explanation:

Step1: Identify the sequence type

This is a geometric - sequence problem. The first - term $a_1 = 15$ (emails sent on day 1), and the common ratio $r = 4$.

Step2: Use the formula for the $n$th term of a geometric sequence

The formula for the $n$th term of a geometric sequence is $a_n=a_1\times r^{n - 1}$. Here, we want to find the number of emails sent on day 10, so $n = 10$.

Step3: Substitute values into the formula

Substitute $a_1 = 15$, $r = 4$, and $n = 10$ into the formula: $a_{10}=15\times4^{10 - 1}$.

Step4: Calculate $4^{9}$

$4^{9}=4\times4\times4\times4\times4\times4\times4\times4\times4 = 262144$.

Step5: Calculate $a_{10}$

$a_{10}=15\times262144 = 15728640$.