Question

Jim has 8 unread emails in his inbox before going on vacation. While on vacation, Jim does not read email. If he receives an average of 22 emails each day, write the nth term of a sequence defining the number of unread emails in his box at the end of day n of his vacation.

Answer 1

`E_n = 8 + 22n`

Explanation:

Since emails arrive at a constant rate of 22 per day, the equation for n-th term can be modeled by a linear relationship of general form:

`E_n = E_0 + k*t`

In this case, E₀ is the initial number of emails unread, 8, k is the rate at which emails arrive, 22 per day, and t is the number of days passed.

At t=n, the number of unread emails is:

`E_n = 8 + 22n`