To describe the relationship between \( t \) (the time in hours) and \( N \) (the number of pages remaining in the book), we can first analyze the table data:
- At \( t = 0 \), \( N = 360 \)
- At \( t = 1 \), \( N = 320 \)
- At \( t = 2 \), \( N = 280 \)
- At \( t = 3 \), \( N = 240 \)
- At \( t = 4 \), \( N = 200 \)
Now, let's examine how \( N \) changes with \( t \). The decrease in the number of pages can be calculated:
- From \( 360 \) to \( 320 \) (decrease of \( 40 \))
- From \( 320 \) to \( 280 \) (decrease of \( 40 \))
- From \( 280 \) to \( 240 \) (decrease of \( 40 \))
- From \( 240 \) to \( 200 \) (decrease of \( 40 \))
The number of pages remaining decreases by \( 40 \) pages each hour. This indicates a linear relationship between \( t \) and \( N \).
We can express this relationship in the general form of a linear equation:
\[ N = mt + b \]
Where:
- \( m \) is the rate of change (slope),
- \( b \) is the initial value (y-intercept).
Here, \( m = -40 \) (since the pages are decreasing), and the initial value \( b = 360 \) (the number of pages at \( t = 0 \)).
Substituting these values into the equation, we get:
\[ N = -40t + 360 \]
Thus, the equation that describes the relationship between \( t \) and \( N \) is:
\[ N = -40t + 360 \]