Question

during a snowstorm, carlo tracked the amount of snow on the ground. when the storm began, there were 1 inches of snow on the ground. snow fell at a constant rate of 2 inches per hour until another 4 inches had fallen. the storm then stopped for 5 hours and then started again at a constant rate of 3 inches per hour for the next 4 hours. as soon as the storm stopped again, the sun came out and melted the snow for the next 4 hours at a constant rate of 5 inches per hour. make a graph showing the inches of snow on the ground over time using the data that carlo collected. click twice to plot a segment. click a segment to delete it. snow on the ground (inches) time since storm began (hours)

Explanation:

Step1: Analyze Initial Snow

Initially, there are 4 inches of snow. So the starting point is (0, 4).

Step2: Snowfall Phase (5 hours, 2 in/h)

For the first 5 hours, snow falls at 2 inches per hour. The amount of snow after 5 hours: \(4 + 2\times5 = 14\) inches. So the end point of this segment is (5, 14).

Step3: Second Snowfall Phase (4 hours, 3 in/h)

Next 4 hours, snow falls at 3 inches per hour. Snow after \(5 + 4 = 9\) hours: \(14 + 3\times4 = 26\) inches. End point: (9, 26).

Step4: Melting Phase (4 hours, 5 in/h)

Next 4 hours, snow melts at 5 inches per hour. Snow after \(9 + 4 = 13\) hours: \(26 - 5\times4 = 6\) inches. End point: (13, 6).
Now, plot the segments: (0,4) to (5,14), (5,14) to (9,26), (9,26) to (13,6).

Answer:

The graph should have three segments: from (0,4) to (5,14) (positive slope 2), (5,14) to (9,26) (positive slope 3), (9,26) to (13,6) (negative slope 5).