To determine the equation that describes the relationship between \( t \) (time in hours) and \( N \) (number of pages remaining), we can analyze the data given in the table:
- At time \( t = 0 \) hours, \( N = 360 \) pages
- At time \( t = 1 \) hour, \( N = 320 \) pages
- At time \( t = 2 \) hours, \( N = 280 \) pages
- At time \( t = 3 \) hours, \( N = 240 \) pages
- At time \( t = 4 \) hours, \( N = 200 \) pages
From this, we can observe the following:
- The number of pages decreases by 40 for each hour that passes. For example:
- From 360 to 320 is a decrease of 40 pages (from \( t = 0 \) to \( t = 1 \))
- From 320 to 280 is a decrease of 40 pages (from \( t = 1 \) to \( t = 2 \))
- This pattern continues for all subsequent hours.
Now, we can identify the slope of the line, which represents the rate of change of pages:
- The slope (rate of change) is \(-40\), indicating that the number of pages remaining decreases by 40 for each hour.
Now, we can use the slope-intercept form of a linear equation:
\[ N = mt + b \]
where \( m \) is the slope and \( b \) is the y-intercept (the number of pages at \( t = 0 \)).
From our data:
- The slope \( m = -40 \)
- The y-intercept \( b = 360 \)
Putting these values into the equation:
\[ N = -40t + 360 \]
Thus, the correct equation that describes the relationship between \( t \) and \( N \) is:
B. \( N = -40t + 360 \)