Question

A city is tracking reports of identity theft. During the first 4 weeks of their study, they find the following number of reports: 11,22,44, and 88 . Which is a possible explicit rule for the number of reports in the nth week?

Answer 1

The possible explicit rule for the number of reports in the nth week is 11 x 2^(n-1).

Step-by-step explanation:

The given problem states that there are a certain number of reports of identity theft each week for the first 4 weeks. The number of reports is 11 for the first week, 22 for the second week, 44 for the third week, and 88 for the fourth week. To find a possible explicit rule for the number of reports in the nth week, we need to look for a pattern or relationship in the data.

Upon examination, we can observe that the number of reports doubles each week. Starting with an initial value of 11, we can express the explicit rule as:

Number of reports in the nth week = 11 x 2^(n-1)

For example, for the fifth week (n = 5), the number of reports is calculated as: 11 x 2^(5-1) = 11 x 2^4 = 11 x 16 = 176.