Question

during a snowstorm, lincoln tracked the amount of snow on the ground. when the storm began, there was no snow on the ground. for the first 3 hours of the storm, snow fell at a constant rate of 3 inches per hour. the storm then stopped for 5 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 lincoln collected.

Explanation:

Step1: Determine time intervals and snow accumulation

• First interval (0 - 3 hours): Snow falls at 3 inches per hour. So, snow accumulation \( y = 3x \) (where \( x \) is time in hours, \( y \) is snow in inches). At \( x = 3 \), \( y = 3\times3 = 9 \) inches.
• Second interval (3 - 8 hours): Storm stops, so snow remains constant at 9 inches. So, \( y = 9 \) for \( 3\leq x\leq8 \).
• Third interval (8 - 10 hours): Snow falls at 2 inches per hour. The initial snow at \( x = 8 \) is 9 inches. So, \( y = 9 + 2(x - 8)=2x - 7 \). At \( x = 10 \), \( y = 2\times10 - 7 = 13 \) inches.

Step2: Plot the graph

• Axes: Let the x - axis represent time (in hours) and the y - axis represent the amount of snow (in inches).
• First segment: From (0, 0) to (3, 9), with a slope of 3.
• Second segment: From (3, 9) to (8, 9), a horizontal line (slope = 0).
• Third segment: From (8, 9) to (10, 13), with a slope of 2.

To create the graph:

Time (x - hours)	Snow (y - inches)
3	9
8	9
10	13

Plot these points and draw the line segments connecting them. The first segment is a straight line from (0,0) to (3,9), the second is a horizontal line from (3,9) to (8,9), and the third is a straight line from (8,9) to (10,13).

Answer:

To graph the snow accumulation over time:

1. Axes Setup:

• X - axis: Time (in hours), ranging from 0 to 10 (since the total time is \( 3 + 5+ 2=10 \) hours).
• Y - axis: Snow (in inches), ranging from 0 to at least 13 (the maximum snow is 13 inches).

1. Plot Key Points:

• (0, 0): Start of the storm, no snow.
• (3, 9): After 3 hours (3 in/h × 3 h = 9 in).
• (8, 9): After 3 + 5 = 8 hours (storm stops, snow remains 9 in).
• (10, 13): After 8 + 2 = 10 hours (9 in + 2 in/h × 2 h = 13 in).

1. Draw Segments:

• From (0, 0) to (3, 9): A line with slope \( 3 \) (constant snowfall).
• From (3, 9) to (8, 9): A horizontal line (no snowfall, constant snow).
• From (8, 9) to (10, 13): A line with slope \( 2 \) (new snowfall rate).

The graph will have three segments: a rising line (0–3 h), a horizontal line (3–8 h), and a rising line (8–10 h).