Question

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 )

Explanation:

Step1: Analyze the relationship

We know that as time \( t \) (in hours) increases, the number of pages remaining \( N \) should decrease. So the coefficient of \( t \) should be negative, eliminating options B and D.

Step2: Check the initial value

When \( t = 0 \) (at the start, no time has passed), the number of pages remaining should be the total number of pages in the book. Let's assume the total pages are 360 (from the constant term). So when \( t = 0 \), \( N = 360 \). For option A: \( N=- 40t-360 \), when \( t = 0 \), \( N=-360 \), which doesn't make sense (can't have negative pages remaining). For option C: \( N=-40t + 360 \), when \( t = 0 \), \( N = 360 \) (correct initial value), and as \( t \) increases, \( N \) decreases (since the coefficient of \( t \) is negative), which matches the relationship between time and remaining pages.

Answer:

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