Question

during a snowstorm, anna tracked the amount of snow on the ground. when the storm began, there were 3 inches of snow on the ground. snow fell at a constant rate of 1 inch per hour until another 2 inches had fallen. the storm then stopped for 6 hours and then started again at a constant rate of 2 inches per hour for the next 2 hours. make a graph showing the inches of snow on the ground over time using the data that anna collected.

Explanation:

Step1: Analyze the first phase

When the storm begins, initial snow is 3 inches. Snow falls at 1 inch per hour until 2 inches fall. Time for this phase: \( t_1=\frac{2}{1} = 2 \) hours. So at \( x = 0 \), \( y=3 \); at \( x = 2 \), \( y=3 + 2=5 \). Plot the segment from (0, 3) to (2, 5).

Step2: Analyze the second phase

Storm stops for 6 hours. So from \( x = 2 \) to \( x=2 + 6=8 \), the snow amount remains 5 inches. Plot the horizontal segment from (2, 5) to (8, 5).

Step3: Analyze the third phase

Snow falls at 2 inches per hour for 2 hours. Time ends at \( x = 8+2 = 10 \). Snow amount at \( x = 10 \): \( y=5+2\times2 = 9 \). Plot the segment from (8, 5) to (10, 9).

Answer:

The graph has three segments:

1. From (0, 3) to (2, 5) (slope 1).
2. From (2, 5) to (8, 5) (horizontal, slope 0).
3. From (8, 5) to (10, 9) (slope 2).