Question

during a snowstorm, casho tracked the amount of snow on the ground. when the storm began, there were 4 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 casho collected.

Explanation:

Step1: Calculate time for first snowfall

Snow needs to fall 4 inches at 2 inches per hour. Time = $\frac{4}{2} = 2$ hours. Snow depth: starts at 4, after 2 hours: $4 + 2\times2 = 8$ inches.

Step2: Storm stops for 5 hours

Time from 2 to $2 + 5 = 7$ hours. Snow depth remains 8 inches.

Step3: Second snowfall (3 in/h for 4h)

Time from 7 to $7 + 4 = 11$ hours. Snow depth: $8 + 3\times4 = 20$ inches.

Step4: Melting (5 in/h for 4h)

Time from 11 to $11 + 4 = 15$ hours. Snow depth: $20 - 5\times4 = 0$ inches.

Step5: Plot intervals

• 0–2h: Line from (0,4) to (2,8) (slope 2).
• 2–7h: Horizontal line from (2,8) to (7,8).
• 7–11h: Line from (7,8) to (11,20) (slope 3).
• 11–15h: Line from (11,20) to (15,0) (slope -5).

Answer:

The graph has four segments:

1. From (0, 4) to (2, 8) (rising, slope 2).
2. From (2, 8) to (7, 8) (horizontal).
3. From (7, 8) to (11, 20) (rising, slope 3).
4. From (11, 20) to (15, 0) (falling, slope -5).