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. a p(0)=0 1 after 20 minutes, the bathtub is empty. b p(4)=10 2 the bathtub starts out with no water. c p(10)=4 3 after 10 minutes, the height of the water is 4 inches. d p(20)=0 4 the height of the water is 10 inches after 4 minutes. 2 function c takes time for its input and gives a particular students monday class for its output. a. use function notation to represent \the student has english at 10:00.\ b. write a statement to describe the meaning of c(11:15)=chemistry.

Explanation:

Problem 1

Step 1: Analyze \( P(0) = 0 \)

The input \( t = 0 \) minutes (start time), and the output \( W = 0 \) inches. This means at the start (0 minutes), the water height is 0 inches, so it matches description 2. So \( A \) matches 2.

Step 2: Analyze \( P(4)=10 \)

Input \( t = 4 \) minutes, output \( W = 10 \) inches. This means after 4 minutes, the water height is 10 inches, so it matches description 4. So \( B \) matches 4.

Step 3: Analyze \( P(10) = 4 \)

Input \( t = 10 \) minutes, output \( W = 4 \) inches. This means after 10 minutes, the water height is 4 inches, so it matches description 3. So \( C \) matches 3.

Step 4: Analyze \( P(20)=0 \)

Input \( t = 20 \) minutes, output \( W = 0 \) inches. This means after 20 minutes, the water height is 0 inches (bathtub is empty), so it matches description 1. So \( D \) matches 1.

The function \( C \) takes time as input and gives the class as output. For the time 10:00, the output is English. So in function notation, it is \( C(10:00)=\text{English} \).

The function \( C \) takes time (input) and gives the class (output). For the input time 11:15, the output is Chemistry. So the statement is: The student has Chemistry at 11:15.

Answer:

\( A \)-2, \( B \)-4, \( C \)-3, \( D \)-1

Problem 2

Part (a)