We are tasked with finding the function that models the scenario described. Here's how we can approach the problem:

Step 1: Identify the variables

• Let $x$ represent the number of hours since the blizzard started.
• Let $y$ represent the number of inches of snow on the ground.

Step 2: Identify key information

• Before the blizzard, there were 12 inches of snow on the ground.
• After the blizzard, there were 36 inches of snow on the ground.
• The blizzard lasted for 6 hours.
• The snow fell at a constant rate during the blizzard.

Step 3: Find the rate of snow accumulation

We can calculate the total amount of snow that fell during the blizzard by subtracting the initial snow from the final amount: $36 \text{ inches} - 12 \text{ inches} = 24 \text{ inches of snow}$

The blizzard lasted for 6 hours, so the rate of snowfall is: $\text{Rate} = \frac{24 \text{ inches}}{6 \text{ hours}} = 4 \text{ inches per hour}$

Step 4: Write the linear function

Since the snow accumulates at a constant rate of 4 inches per hour, the equation for the number of inches of snow, $y$, as a function of the number of hours, $x$, is: $y = 4x + 12$ Where:

• The slope is 4 (the rate of snow accumulation),
• The y-intercept is 12, representing the initial snow on the ground before the blizzard.

Step 5: Match with the options

This matches option B: $y = 4x + 12$

Conclusion:

The correct function is $y = 4x + 12$, which is Option B.

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Would you like more details on how we derived this, or do you have any other questions?

Here are 5 related questions:

1. What does the slope represent in this context?
2. How can we find the equation of a line given two points?
3. What would happen if the snow accumulation rate were different?
4. How can we graph this equation?
5. What does the y-intercept tell us in this scenario?

Tip: When working with word problems, it's helpful to identify known values first (like the initial conditions) and then determine how the situation changes (like the rate of snow accumulation).