To find the equation that describes the relationship between time \( t \) (in hours) and the number of pages \( N \) remaining in the book, we can analyze the data provided.
From the table, we see the number of pages remaining decreases linearly:
- At \( t = 0 \): \( N = 360 \)
- At \( t = 1 \): \( N = 320 \)
- At \( t = 2 \): \( N = 280 \)
- At \( t = 3 \): \( N = 240 \)
- At \( t = 4 \): \( N = 200 \)
The change in the number of pages remaining over each hour is consistent:
- From 360 to 320 (decrease of 40 pages)
- From 320 to 280 (decrease of 40 pages)
- From 280 to 240 (decrease of 40 pages)
- From 240 to 200 (decrease of 40 pages)
This means that the slope of the line (the rate of change of \( N \) with respect to \( t \)) is -40 pages per hour.
Since the relationship is linear, we can express it in the form: \[ N = mt + b \] where \( m \) is the slope and \( b \) is the y-intercept.
From our observations:
- The slope \( m = -40 \)
- The initial number of pages (when \( t = 0 \)) is \( b = 360 \)
Putting this into the equation format: \[ N = -40t + 360 \]
This corresponds to option B.
Thus, the correct equation is: B. \( N = -40t + 360 \).