Question

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.N=-40t-360

B. N=-40t+360

C.N=40t-360

D.N=40t+360

Answer 1

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. \( N = -40t + 360 \)**.