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Water is filling a pool. The function
W gives the pool's water level (in meters) after
t minutes.
What is the best interpretation for the following statement?
The slope of the line tangent to the graph of
W at
t=5 is equal to 0.1 .
Choose 1 answer:
(A) After 5 minutes, the pool is being filled at a rate of 0.1 meters per minute.
B The pool is being filled at a rate of
(0.1)/(5) meters per minute.
(C) After 5 minutes, the pool's water level is 0.1 meters.
(D) After 5 minutes, the pool is being filled at a rate of 0.1 minutes per meter.

Water is filling a pool. The function $W$ gives the pool's water level (in meters) after $t$ minutes. $\newline$ What is the best interpretation for the following statement? $\newline$ The slope of the line tangent to the graph of $W$ at $t=5$ is equal to $0$ . $1$ . $\newline$ Choose $1$ answer: $\newline$ (A) After $5$ minutes, the pool is being filled at a rate of $0$ . $1$ meters per minute. $\newline$ (B) The pool is being filled at a rate of $\frac{0.1}{5}$ meters per minute. $\newline$ (C) After $5$ minutes, the pool's water level is $0$ . $1$ meters. $\newline$ (D) After $5$ minutes, the pool is being filled at a rate of $0$ . $1$ minutes per meter.

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Interpreting Linear Expressions

Full solution

Q. Water is filling a pool. The function

W

gives the pool's water level (in meters) after

t

minutes.

\newline

What is the best interpretation for the following statement?

\newline

The slope of the line tangent to the graph of

W

at

t=5

is equal to

0

.

1

.

\newline

Choose

1

answer:

\newline

(A) After

5

minutes, the pool is being filled at a rate of

0

.

1

meters per minute.

\newline

(B) The pool is being filled at a rate of

\frac{0.1}{5}

meters per minute.

\newline

(C) After

5

minutes, the pool's water level is

0

.

1

meters.

\newline

(D) After

5

minutes, the pool is being filled at a rate of

0

.

1

minutes per meter.

Rate of Change Definition: The slope of a line tangent to a function at a given point represents the rate of change of the function at that point.
Water Level Slope at $t=5$ : Since $W$ represents the water level after $t$ minutes, the slope at $t=5$ represents the rate at which the water level is changing at $5$ minutes.
Interpretation of Slope: The slope given is $0.1$ , which means the water level is rising at a rate of $0.1$ meters per minute at $t=5$ .
Pool Filling Rate: Therefore, the correct interpretation of the statement is that after $5$ minutes, the pool is being filled at a rate of $0.1$ meters per minute.

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