To find 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.
From the table, we can note the following:
- At \( t = 0 \) hours, \( N = 360 \) pages
- At \( t = 1 \) hour, \( N = 320 \) pages
- At \( t = 2 \) hours, \( N = 280 \) pages
- At \( t = 3 \) hours, \( N = 240 \) pages
- At \( t = 4 \) hours, \( N = 200 \) pages
Now, let's observe how the number of pages remaining changes with time:
- From 0 to 1 hour:
- Decrease from 360 to 320: \( 360 - 320 = 40 \) pages
- From 1 to 2 hours:
- Decrease from 320 to 280: \( 320 - 280 = 40 \) pages
- From 2 to 3 hours:
- Decrease from 280 to 240: \( 280 - 240 = 40 \) pages
- From 3 to 4 hours:
- Decrease from 240 to 200: \( 240 - 200 = 40 \) pages
The pages remaining decrease by 40 pages per hour. Therefore, the slope of the equation will be \(-40\) (since the number of pages is decreasing).
The initial number of pages when \( t = 0 \) is 360.
The equation of a line can be expressed in the form:
\[ N = mt + b \]
where:
- \( m \) is the slope,
- \( b \) is the y-intercept (the value of \( N \) when \( t = 0 \)).
So in this case:
- \( m = -40 \),
- \( b = 360 \).
Thus, the equation relating \( t \) and \( N \) is:
\[ N = -40t + 360 \]
This matches option B: \( N = -40t + 360 \).
Therefore, the correct answer is:
B. \( N = -40t + 360 \).
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