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Find the rate of change for each day and compare the results.
Sunday
We are asked to determine which day had a greater rate of change. To do so, we need to find the rates of change for both Saturday and Sunday and compare the results. We will start with Saturday. The amount of rainfall on Saturday is shown in the following table.
Let's analyze how the amount of rainfall on Saturday changes over time.
On Saturday, the amount of rainfall increases by 1.5 inches every hour. Let's use this information to write a unit rate, which is also the rate of change. Change in inches/Change in time=1.5inches/1hour Therefore, the rate of change for Saturday is 1.5 inches per hour. Next, we will analyze the amount of rainfall on Sunday. To do so, let's take a look at the following graph.
Recall that if we are given two points that lie on a line, we can calculate the rate of change of the line using the following formula. Rate of change=Change in y/Change in x We can use any two points on the line to find the rate of change. Let's use (1,2) and (2,4).
We can substitute the values from the points into our formula to calculate the rate of change. Change in inches/Change in time=(4-2)inches/(2-1)hours= 2inches/1hour We got that the rate of change for Sunday is 2 inches per hour. Now we can finally compare the rates of change for Saturday and Sunday. ccc Saturday & & Sunday 1.5 inches per hour & < & 2 inches per hour As we can see, the rate of change for Sunday is greater than for Saturday.
