The problem describes the height of water in a bathtub, $w$, as a function of time, $t$. The function is represented by $P$. Height is measured in inches, and time is measured in minutes. The goal is to match each statement in function notation with its corresponding description.

1. Problem Description

The problem describes the height of water in a bathtub, $w$, as a function of time, $t$. The function is represented by $P$. Height is measured in inches, and time is measured in minutes. The goal is to match each statement in function notation with its corresponding description.

2. Solution Steps

We are given four function notations and four descriptions. We need to match each function notation with the correct description.

A. $P(0) = 0$: This means at time $t=0$, the height of the water is 0 inches. This corresponds to the description "The bathtub starts out with no water." Thus, A matches with

2. B. $P(4) = 10$: This means at time $t=4$ minutes, the height of the water is 10 inches. This corresponds to the description "The height of the water is 10 inches after 4 minutes." Thus, B matches with

4. C. $P(10) = 4$: This means at time $t=10$ minutes, the height of the water is 4 inches. This corresponds to the description "After 10 minutes, the height of the water is 4 inches." Thus, C matches with

3. D. $P(20) = 0$: This means at time $t=20$ minutes, the height of the water is 0 inches. This corresponds to the description "After 20 minutes, the bathtub is empty." Thus, D matches with

1.

3. Final Answer

A matches with

2. B matches with

4. C matches with

3. D matches with 1.