Question

1. the height of water in a bathtub, w, is a function of time, t. let p represent this function. height is measured in inches and time in minutes. match each statement in function notation with a description.

function notation	description
b. $p(4)=10$	ii. the bathtub starts out with no water.
c. $p(10)=4$	iii. after 10 minutes, the height of the water is 4 inches.
d. $p(20)=0$	iv. the height of the water is 10 inches after 4 minutes.

Explanation:

for each match:

Part a: \( P(0) = 0 \)

The input \( t = 0 \) (time in minutes) and output \( P(0)=0 \) (height in inches) means at the start (0 minutes), the bathtub has no water. So match with ii. The bathtub starts out with no water.

Part b: \( P(4) = 10 \)

Input \( t = 4 \) minutes, output height is 10 inches. So match with iv. The height of the water is 10 inches after 4 minutes.

Part c: \( P(10) = 4 \)

Input \( t = 10 \) minutes, output height is 4 inches. So match with iii. After 10 minutes, the height of the water is 4 inches.

Part d: \( P(20) = 0 \)

Input \( t = 20 \) minutes, output height is 0 inches. So match with i. After 20 minutes, the bathtub is empty.

Answer:

a. \( P(0) = 0 \) matches ii. The bathtub starts out with no water.
b. \( P(4) = 10 \) matches iv. The height of the water is 10 inches after 4 minutes.
c. \( P(10) = 4 \) matches iii. After 10 minutes, the height of the water is 4 inches.
d. \( P(20) = 0 \) matches i. After 20 minutes, the bathtub is empty.