Question

A company is tracking a number of complaints received on its website. During the first 4 months, they

record the following numbers of complaints: 18, 22, 26, 30. What is the explicit rule for the number of
complaints they will received in the nth month? After how many months will the complaints reach 126?

Answer 1

To find the explicit rule for the number of complaints received in the nth month, we can observe the pattern in the given data. The number of complaints increases by 4 each month.

So, we can write the explicit rule as follows:

Number of complaints (n) = 18 + 4(n - 1)

To find the number of months it will take for the complaints to reach 126, we can set up an equation:

18 + 4(n - 1) = 126

Simplifying the equation:

4(n - 1) = 126 - 18

4(n - 1) = 108

n - 1 = 27

n = 28

Therefore, it will take 28 months for the number of complaints to reach 126.