Monique is reading a book. The table shows how the number of pages remaining in the book is changing over time. READING A BOOK Time (hours) Number of Pages Remaining 0 360 1 320 2 280 3 240 4 200 Which equation describes the relationship between t, the time in hours, and N, the number of pages remaining in the book? A .

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

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:

\[
N = 360 - 40t
\]