Question

1. the amount of rainfall over one week is shown in the graph to the right. the rainfall, r, is measured in centimeters, and t is measured in days. each interval from 0 to 1 on the t - axis represents the 24 - hour period for day 1, the interval from 1 to 2 represents the 24 - hour period for day 2, etc.

a.) on what days did it rain? on what days did it not rain?
days it rained: 0 to 1, 2 to 3, and 5 to 6
days it did not rain: 1 to 2, 4 to 5, and 6 to 7
b.) on what day(s) was the rain the heaviest? explain how you know.
days 5 - 7 produced the heaviest rain since the rainfall (cm) increased constantly.
c.) is it possible for the function to decrease? explain.

Explanation:

Step1: Analyze rainfall graph

The graph shows rainfall over time. Rain occurs when the rainfall - value (r) is increasing or non - zero.

Step2: Determine heaviest rain

The steepest increase in the graph indicates the heaviest rain. Here, the increase from day 5 to day 7 is the steepest.

Step3: Consider function decrease

Rainfall is a non - negative quantity. In the context of this problem, once rain has fallen, it cannot be "undone" in terms of the total accumulated rainfall over time. So, the function representing the total rainfall over time cannot decrease.

Answer:

a. Days it rained: 0 to 1, 2 to 3, and 5 to 6; Days it did not rain: 1 to 2, 4 to 5, and 6 to 7
b. Day 5 - 7; because the slope of the graph (rate of change of rainfall) is the steepest during this period.
c. No; rainfall is a non - negative cumulative quantity and cannot decrease over time in this context.