The Correct Answer and Explanation is:1
Based on the graph provided, the correct answer is 1.5. This number represents the rate at which the bathtub is filling with water, measured in gallons per minute.
The question asks for the rate of change for the interval between 0 and 10 minutes. In the context of a graph, the rate of change is equivalent to the slope of the line. The formula for calculating slope is the change in the vertical axis (y) divided by the change in the horizontal axis (x).
First, we must identify the two points on the graph that correspond to the specified time interval. The interval begins at 0 minutes. At this point, the tub is empty, so the starting coordinate is (0 minutes, 0 gallons). The interval ends at 10 minutes. By looking at the graph, we can see that at the 10 minute mark on the x-axis, the line reaches a value of 15 on the y-axis. This gives us the ending coordinate of (10 minutes, 15 gallons).
Next, we apply the slope formula to these two points. The change in volume (y-axis) is the final volume minus the initial volume, which is 15 gallons minus 0 gallons, resulting in a change of 15 gallons. The change in time (x-axis) is the final time minus the initial time, which is 10 minutes minus 0 minutes, resulting in a change of 10 minutes.
To find the rate, we divide the change in volume by the change in time:
Rate of Change = 15 gallons / 10 minutes = 1.5 gallons per minute.
This value of 1.5 signifies that for every minute that passes during this initial 10 minute period, 1.5 gallons of water are added to the tub. It is the constant speed at which the bathtub is filling. After 10 minutes, the graph becomes a horizontal line, indicating the rate of change is zero and the water has been turned off.
