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

1 answer

To find the equation that describes the relationship between time \( t \) (in hours) and the number of pages \( N \) remaining in the book, we can analyze the data provided.

From the table, we see the number of pages remaining decreases linearly:

  • At \( t = 0 \): \( N = 360 \)
  • At \( t = 1 \): \( N = 320 \)
  • At \( t = 2 \): \( N = 280 \)
  • At \( t = 3 \): \( N = 240 \)
  • At \( t = 4 \): \( N = 200 \)

The change in the number of pages remaining over each hour is consistent:

  • From 360 to 320 (decrease of 40 pages)
  • From 320 to 280 (decrease of 40 pages)
  • From 280 to 240 (decrease of 40 pages)
  • From 240 to 200 (decrease of 40 pages)

This means that the slope of the line (the rate of change of \( N \) with respect to \( t \)) is -40 pages per hour.

Since the relationship is linear, we can express it in the form: \[ N = mt + b \] where \( m \) is the slope and \( b \) is the y-intercept.

From our observations:

  • The slope \( m = -40 \)
  • The initial number of pages (when \( t = 0 \)) is \( b = 360 \)

Putting this into the equation format: \[ N = -40t + 360 \]

This corresponds to option B.

Thus, the correct equation is: B. \( N = -40t + 360 \).