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P gives the lion population at a certain game reserve
t years after the reserve was established.
What is the best interpretation for the following statement?
The value of the derivative of
P at
t=6 is equal to 12 .
Choose 1 answer:
(A) After 6 years, the lion population grows at a rate of 12 lions.
(B) After 6 years, the lion population grows at a rate of 12 lions per year.
(C) The lion population grows at a rate of 12 lions per 6 years.
(D) After 6 years, there were 12 lions in the reserve.

$P$ gives the lion population at a certain game reserve $t$ years after the reserve was established. $\newline$ What is the best interpretation for the following statement? $\newline$ The value of the derivative of $P$ at $t=6$ is equal to $12$ . $\newline$ Choose $1$ answer: $\newline$ (A) After $6$ years, the lion population grows at a rate of $12$ lions. $\newline$ (B) After $6$ years, the lion population grows at a rate of $12$ lions per year. $\newline$ (C) The lion population grows at a rate of $12$ lions per $6$ years. $\newline$ (D) After $6$ years, there were $12$ lions in the reserve.

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Interpreting Linear Expressions

Full solution

Q.

P

gives the lion population at a certain game reserve

t

years after the reserve was established.

\newline

What is the best interpretation for the following statement?

\newline

The value of the derivative of

P

at

t=6

is equal to

12

.

\newline

Choose

1

answer:

\newline

(A) After

6

years, the lion population grows at a rate of

12

lions.

\newline

(B) After

6

years, the lion population grows at a rate of

12

lions per year.

\newline

(C) The lion population grows at a rate of

12

lions per

6

years.

\newline

(D) After

6

years, there were

12

lions in the reserve.

Rate of Change Definition: The derivative of $P$ with respect to $t$ represents the rate of change of the lion population with respect to time.
Derivative at $t=6$ : At $t=6$ , the derivative being $12$ means that at that specific time, the population is increasing at a rate of $12$ lions per year.
Instantaneous Rate Clarification: This rate of change is an instantaneous rate, not an average over a period of time, so it's per year, not per $6$ years.
Correct Interpretation: Therefore, the correct interpretation of the derivative value is that after $6$ years, the lion population grows at a rate of $12$ lions per year.

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