c How is the rain rate changing? Sketch the graphs by parts.
A
a It would be a continuous graph.
B
b The graph would be a horizontal line.
C
c
Practice makes perfect
a We know that the rain gauge will be making measurements during the 24 hour period. Also, since the input of this relation is time, it can take any value from 0 to 24 hours. Therefore, every input will have its corresponding output and their graph will be a continuous stroke.
b If it rained at a rate of of 0.1 inches per hour for the whole 24 hour period, then the rain rate is always the same. Therefore, the graph would be a horizontal line.
c Now we need to describe the graph corresponding to a rain at a rate of 0.1 inch per hour for 6 hours. Then, it stops raining for the next 6 hours. Finally, it starts raining at a rate of 0.2 inches per hour for 12 hours. Let's analyze this by parts.
It rains at a constant rate of 0.1 inch per hour for 6 hours.
It stops raining for 12 hr.
It starts raining at a rate of 0.2 inches per hour for 12 hours.
Notice that when it stopped and when it started raining we can see a steep descent and rise respectively, but not a jump from a horizontal line to another horizontal line. This is because this transition does not happen instantly.
