Let's work through the questions in the image one by one:

1. If it continues to snow at the same rate, how many inches of snow would you expect after 6.5 hours?

We can calculate the rate of snowfall using the information provided in the table. After 2 hours, 4 inches of snow has fallen. Thus, the rate of snowfall is:

$\text{Rate of snowfall} = \frac{4 \, \text{inches}}{2 \, \text{hours}} = 2 \, \text{inches per hour}$

At this rate, after 6.5 hours:

$\text{Snowfall after 6.5 hours} = 6.5 \, \text{hours} \times 2 \, \text{inches per hour} = 13 \, \text{inches}$

So, after 6.5 hours, 13 inches of snow will have fallen.

2. Write an equation that gives the amount of snow that has fallen after $t$ hours at this rate.

The snowfall rate is $2 \, \text{inches per hour}$, so the total snowfall $S(t)$ after $t$ hours can be expressed as:

$S(t) = 2t$

Where:

• $S(t)$ is the amount of snow (in inches) after $t$ hours.
• $t$ is the time (in hours).

3. How many inches of snow will fall in 24 hours if it continues to snow at this rate?

Using the equation $S(t) = 2t$, we substitute $t = 24$ hours:

$S(24) = 2 \times 24 = 48 \, \text{inches}$

So, 48 inches of snow will fall in 24 hours.

Would you like further details on any of these calculations?

Here are some related questions:

1. What would be the total snowfall after 10 hours?
2. How would the equation change if the snowfall rate was 1.5 inches per hour?
3. Can we determine how long it would take for 30 inches of snow to accumulate?
4. If the snowfall rate doubled, what would the new equation for snowfall be?
5. How would you calculate the amount of snow that falls between specific time intervals, e.g., between 3 and 5 hours?

Tip: In real-world problems involving rates, ensure you understand how to calculate the rate of change (e.g., inches per hour) and apply it consistently over time.