Question

Chain emails are emails with a message suggesting you will have good luck if you forward the email on to others.

Suppose a student started a chain email by sending the message to 3 friends and asking those friends to each send the
same email to 3 more friends exactly 1 day after receiving it.
b. Which day is the first day that the number of people receiving the email exceeds 100?

Answer 1

To find the first day the number of people receiving the email exceeds 100, we can use exponential growth. By representing the number of people receiving the email on day 0 and day 1, and using the formula Nt = N0 * (3^t), we can solve for the smallest t such that Nt > 100.

Step-by-step explanation:

To determine the first day that the number of people receiving the email exceeds 100, we can use exponential growth. Let's represent the number of people receiving the email on day 0 as N0 = 1 (since the student started the chain email) and the number of people receiving the email on day 1 as N1 = 3 (since each friend received it). We can use the formula Nt = N0 * (3^t), where t is the number of days since the start. We need to find the smallest t such that Nt > 100.

1. Substitute N0 = 1 and Nt = 3^t into the inequality 3^t > 100.
2. Take the base-3 logarithm of both sides to solve for t: log base 3 of (3^t) > log base 3 of 100.
3. Simplify the equation and solve for t: t > log base 3 of 100 / log base 3 of 3.
4. Using a calculator, evaluate t to find the smallest whole number greater than the result.

Therefore, the first day that the number of people receiving the email exceeds 100 is the smallest whole number greater than the result obtained from step 3.

Answer 2

b.

starts with student-day one

3*3=9-day two

9*3=27-day three

27*3=81-day four

81*3= over 100- day five

it's day 5 unless you count the first student sending the message as day 0, if so then your answer is day 4