To find the equation that describes the relationship between time \( t \) (in hours) and the number of pages remaining \( N \), we can analyze the data from the table:
- 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.
Next, let's look at how many pages Monique reads per hour:
- From \( t = 0 \) to \( t = 1 \): \( 360 - 320 = 40 \) pages
- From \( t = 1 \) to \( t = 2 \): \( 320 - 280 = 40 \) pages
- From \( t = 2 \) to \( t = 3 \): \( 280 - 240 = 40 \) pages
- From \( t = 3 \) to \( t = 4 \): \( 240 - 200 = 40 \) pages
Monique reads 40 pages per hour consistently.
Now we can form the equation. The initial number of pages is 360, and for every hour \( t \), she reads 40 pages. Therefore, the relationship can be expressed as:
\[ N(t) = 360 - 40t \]
where:
- \( N(t) \) is the number of pages remaining after \( t \) hours,
- 360 is the initial number of pages,
- 40 is the number of pages read per hour,
- \( t \) is the number of hours.
Thus, the equation that describes the relationship is:
\[ N = 360 - 40t \]