Question

practice problems
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 student’s 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) = \text{chemistry} ).

Explanation:

Problem 1

• For \( P(0) = 0 \): The input \( t = 0 \) represents the start time. So when \( t = 0 \), \( W = 0 \) means the bathtub starts with no water, which matches description 2.
• For \( P(4)=10 \): The input \( t = 4 \) (minutes) and output \( W = 10 \) (inches) means after 4 minutes, the water height is 10 inches, matching description 4.
• For \( P(10) = 4 \): Input \( t = 10 \) (minutes) and output \( W = 4 \) (inches) means after 10 minutes, water height is 4 inches, matching description 3.
• For \( P(20)=0 \): Input \( t = 20 \) (minutes) and output \( W = 0 \) (inches) means after 20 minutes, the bathtub is empty, matching description 1.

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

Function \( C \) takes time as input and gives the class as output. So \( C(11:15)=\text{Chemistry} \) means at 11:15, the student has Chemistry class.

Answer:

A - 2, B - 4, C - 3, D - 1

Problem 2a