Question

what has been the average hourly change in the number of pages read by kathleen over the past 4 hours?
a. 36
b. 40
c. 45
d. 96
(hour: 0,1,2,3,4; pages read: 0,36,78,113,158)

Explanation:

Step1: Determine total change in pages

At hour 0, pages read = 0. At hour 4, pages read = 158. Total change = \( 158 - 0 = 158 \)? Wait, no, wait. Wait the table: Hour 0: 0, Hour 1: 36, Hour 2:78, Hour 3:113, Hour 4:158. Wait, the question is over past 4 hours. So time from hour 0 to hour 4? Wait, no, "past 4 hours" – so from hour 0 to hour 4, that's 4 hours? Wait, no, the time intervals: from hour 0 to hour 1 is 1 hour, hour 1 to 2 is 1 hour, etc. Wait, the average hourly change is the slope of the line, or the average rate of change. The formula for average rate of change is \( \frac{\text{Final Pages} - \text{Initial Pages}}{\text{Final Hour} - \text{Initial Hour}} \). Initial at hour 0: 0 pages. Final at hour 4: 158 pages? Wait no, wait the table: Hour 0: 0, Hour 1: 36, Hour 2:78, Hour 3:113, Hour 4:158. Wait, but maybe the question is over the past 4 hours, meaning from hour 0 to hour 4, which is 4 hours. Wait, but let's check the options. The options are 36,40,45,96. Wait, maybe I misread. Wait, maybe the initial is hour 0 (0 pages) and final is hour 4 (158 pages)? No, 158/4 is 39.5, close to 40. Wait, maybe the table is: Hour 0:0, Hour 1:36, Hour 2:78, Hour 3:113, Hour 4:158. Wait, the average hourly change is (158 - 0)/4 = 39.5, which is approximately 40. So option B.
Wait, let's recalculate. The average rate of change is (final - initial)/(time). Initial pages at hour 0: 0. Final pages at hour 4: 158. Time elapsed: 4 - 0 = 4 hours. So \( \frac{158 - 0}{4} = \frac{158}{4} = 39.5 \), which is closest to 40 (option B).

Step2: Verify with options

The options are A.36, B.40, C.45, D.96. 39.5 is approximately 40, so the answer is B.

Answer:

B. 40