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Multiple Choice 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

1 answer

To determine the correct equation that describes the relationship between time (t) and the number of pages remaining (N), let's first analyze the data given:

  • 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.

From the data, we can see that every hour, the number of pages remaining decreases by 40 pages (e.g., from 360 to 320 is a decrease of 40).

The relationship can be represented as:

  1. The slope (rate of change) of the line is \(-40\) (decrease by 40 pages/hour).
  2. The initial value (y-intercept) when \( t = 0 \) is 360.

Putting this together, the equation in slope-intercept form \( N = mt + b \) is: \[ N = -40t + 360 \]

Therefore, the correct answer is:

B. N = -40t + 360