The height of snow on Jasper’s driveway is modeled by the function:

$f(x) = 5 + \frac{2}{3}x$

where $f(x)$ is the height of snow in inches, and $x$ is the number of hours after midnight.

To determine if Jasper should turn off his alarm, we need to check the height of the snow at 6 AM, which is 6 hours after midnight. That means $x = 6$.

Substitute $x = 6$ into the function:

$f(6) = 5 + \frac{2}{3}(6)$

First, calculate $\frac{2}{3} \times 6$:

$\frac{2}{3} \times 6 = 4$

Now, substitute this into the equation:

$f(6) = 5 + 4 = 9$

At 6 AM, the height of the snow will be 9 inches. Since this is less than the required 12 inches for school cancellation, Jasper should not turn off his alarm, as school will likely not be canceled based on the given conditions.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. What would the height of the snow be at 7 AM?
2. How many hours after midnight will the snow reach 12 inches?
3. If the snow started falling at a faster rate, say $\frac{3}{4}x$, how would that change the outcome?
4. What does the constant 5 in the equation represent?
5. How long will it take for the snow to reach 15 inches?

Tip: For word problems involving time and rate, always ensure you’re interpreting the variables (like time) in context to avoid confusion.