We are given that Mason devours 4 slices of pizza every 2 minutes, starting after eating his first slice. We need to find a linear function $P(t)$ that represents the total number of pizza slices Mason eats after $t$ minutes.

Step 1: Understand the situation

• Mason eats his first slice, and then he continues to eat 4 slices every 2 minutes.
• This creates a constant rate of pizza consumption after the first slice.

Step 2: Define the rate

Mason's rate of eating is 4 slices every 2 minutes, which simplifies to a rate of 2 slices per minute. So, after the first slice, his consumption increases by 2 slices per minute.

Step 3: Create the linear function

• Mason eats 1 slice at $t = 0$ (the first slice).
• Then for each minute after that, he eats 2 slices.

Thus, the total number of pizza slices Mason eats as a function of time $t$ in minutes is:

$P(t) = 1 + 2t$

Where:

• $P(t)$ is the total number of pizza slices after $t$ minutes,
• $t$ is the time in minutes.

Step 4: Find how long it will take Mason to devour 217 pizza slices

We are given $P(t) = 217$. Substituting into the equation $P(t) = 1 + 2t$:

$217 = 1 + 2t$

Now, solve for $t$: $217 - 1 = 2t$ $216 = 2t$ $t = \frac{216}{2} = 108$

Final Answer:

It will take Mason 108 minutes to devour 217 pizza slices.

Would you like a more detailed explanation or have any further questions?

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Here are 5 related questions you might find interesting:

1. How many slices will Mason eat in the first 10 minutes?
2. If Mason takes a 5-minute break every 30 minutes, how many slices will he eat in 2 hours?
3. What is the slope of the linear function $P(t)$, and what does it represent in this scenario?
4. How would the function change if Mason started eating with 2 slices instead of 1 at $t = 0$?
5. If Mason could only eat for 50 minutes, how many slices would he consume in that time?

Tip: In any problem involving constant rates, the slope of a linear function represents the rate of change—how quickly something is increasing or decreasing over time.