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The function
D gives the day length, in minutes, of the
n^("th ") day of the year in Juneau, Alaska.
What is the best interpretation for the following statement?

D^(')(10)=3
Choose 1 answer:
(A) On January 10, the day length is increasing at a rate of 3 minutes per day.
(B) On January 10 , the day is 3 minutes long.
(C) On January 10 , the day length is increasing at a rate of 3 days per minute.
(D) Until January 10, the day length is increasing at a rate of 3 minutes per day.

The function $D$ gives the day length, in minutes, of the $n^{\text {th }}$ day of the year in Juneau, Alaska. $\newline$ What is the best interpretation for the following statement? $\newline$ $D^{\prime}(10)=3$ $\newline$ Choose $1$ answer: $\newline$ (A) On January $10$ , the day length is increasing at a rate of $3$ minutes per day. $\newline$ (B) On January $10$ , the day is $3$ minutes long. $\newline$ (C) On January $10$ , the day length is increasing at a rate of $3$ days per minute. $\newline$ (D) Until January $10$ , the day length is increasing at a rate of $3$ minutes per day.

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Evaluate a linear function: word problems

Full solution

Q. The function

D

gives the day length, in minutes, of the

n^{\text {th }}

day of the year in Juneau, Alaska.

\newline

What is the best interpretation for the following statement?

\newline

D^{\prime}(10)=3

\newline

Choose

1

answer:

\newline

(A) On January

10

, the day length is increasing at a rate of

3

minutes per day.

\newline

(B) On January

10

, the day is

3

minutes long.

\newline

(C) On January

10

, the day length is increasing at a rate of

3

days per minute.

\newline

(D) Until January

10

, the day length is increasing at a rate of

3

minutes per day.

Derivative Interpretation: $D^{'}(10)$ represents the derivative of the day length function on the $10$ th day, which means it's the rate of change of day length on that day.
Positive Derivative: Since the derivative is positive ( $3$ ), it indicates that the day length is increasing.
Rate of Change: The rate is given in minutes per day, so for every day after the $10^{th}$ , the day length is $3$ minutes longer than the previous day.
Correct Interpretation: The correct interpretation is that on January $10$ , the day length is increasing at a rate of $3$ minutes per day.

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