To determine the correct equation that describes the relationship between time (t) and the number of pages remaining (N), we can analyze the provided data in the table.
Looking at the change in the number of pages remaining:
- From 0 to 1 hour, N decreases from 360 to 320, which is a change of -40 pages.
- From 1 to 2 hours, N decreases from 320 to 280, another change of -40 pages.
- This continues consistently: N decreases by 40 pages for every hour.
This indicates that the number of pages remaining decreases linearly with time, at a rate of -40 pages per hour.
Now, let's set up the relationship. The general form of a linear equation is: \[ N = mt + b \] where:
- \( m \) is the rate of change (slope), and
- \( b \) is the y-intercept (the number of pages remaining at t = 0).
In this case:
- The rate of change \( m \) = -40 (since the number of pages is decreasing).
- At time \( t = 0 \) (the beginning), \( N = 360 \).
Substituting these values into the equation gives: \[ N = -40t + 360 \]
Rearranging this to match the typical form, we get: \[ N = 360 - 40t \]
However, none of the answer choices provided are in that exact form. Let's check the answers provided:
A. \( N = -40t - 360 \) (Incorrect) B. \( N = -40t + 360 \) (Correct, but has a typo in "B", should have "plus" instead of "equal") C. \( N = 40t + 360 \) (Incorrect) D. \( N = 40t - 360 \) (Incorrect)
Therefore, the answer is closest to "B" when correcting it to: \[ N = -40t + 360 \]
So the best answer here is: B. \( N = -40t + 360 \) with the interpretation that it's the correct form.