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Due to the tide, the water level rises and falls daily in Buzzard's Bay.
D gives the depth of the water, in meters,
t hours after midnight on a certain day.
What is the best interpretation for the following statement?
The value of the derivative of
D at
t=8 is equal to -0.5 .
Choose 1 answer:
(A) At 8 a.m. the water level decreased at a rate of 0.5 meters per hour.
(B) At 8 a.m. the water level decreased at a rate of 0.5 meters.
(C) At 8 a.m. the water level was 0.5 meters below sea level.
(D) Until 8 a.m. the water level decreased at a rate of 0.5 meters per hour.

Due to the tide, the water level rises and falls daily in Buzzard's Bay. $D$ gives the depth of the water, in meters, $t$ hours after midnight on a certain day. $\newline$ What is the best interpretation for the following statement? $\newline$ The value of the derivative of $D$ at $t=8$ is equal to $-0$ . $5$ . $\newline$ Choose $1$ answer: $\newline$ (A) At $8$ a.m. the water level decreased at a rate of $0$ . $5$ meters per hour. $\newline$ (B) At $8$ a.m. the water level decreased at a rate of $0$ . $5$ meters. $\newline$ (C) At $8$ a.m. the water level was $0$ . $5$ meters below sea level. $\newline$ (D) Until $8$ a.m. the water level decreased at a rate of $0$ . $5$ meters per hour.

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Interpreting Linear Expressions

Full solution

Q. Due to the tide, the water level rises and falls daily in Buzzard's Bay.

D

gives the depth of the water, in meters,

t

hours after midnight on a certain day.

\newline

What is the best interpretation for the following statement?

\newline

The value of the derivative of

D

at

t=8

is equal to

-0

.

5

.

\newline

Choose

1

answer:

\newline

(A) At

8

a.m. the water level decreased at a rate of

0

.

5

meters per hour.

\newline

(B) At

8

a.m. the water level decreased at a rate of

0

.

5

meters.

\newline

(C) At

8

a.m. the water level was

0

.

5

meters below sea level.

\newline

(D) Until

8

a.m. the water level decreased at a rate of

0

.

5

meters per hour.

Derivative Definition: The derivative of $D$ with respect to $t$ represents the rate of change of the water depth with respect to time.
Derivative at $t=8$ : At $t=8$ , which is $8$ a.m., the derivative is $-0.5$ . This means the water level is changing at a rate of $-0.5$ meters per hour at that time.
Negative Derivative: Since the derivative is negative, it indicates that the water level is decreasing, not increasing.
Interpretation of Derivative at $t=8$ : The correct interpretation of the derivative being $-0.5$ at $t=8$ is that at $8$ a.m., the water level decreased at a rate of $0.5$ meters per hour.

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