$f(x)=2,500(0.66)^{x}$ $\newline$ The equation models $f$ , the number of new social media posts associated with a trending hashtag $x$ days after its peak popularity. Which of the following statements is the best interpretation of the ordered pair $(3,719)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) The trending hashtag maintains $719$ new social media posts per day for $3$ days. $\newline$ (B) The number of new social media posts associated with the trending hashtag increases by $719$ per day for $3$ days. $\newline$ (C) $3$ new social media posts associated with the trending hashtag are made $719$ days after the hashtag's peak popularity. $\newline$ (D) $719$ new social media posts associated with the trending hashtag are made $3$ days after the hashtag's peak popularity.

Full solution

f(x)=2,500(0.66)^{x}

\newline

The equation models

f

, the number of new social media posts associated with a trending hashtag

x

days after its peak popularity. Which of the following statements is the best interpretation of the ordered pair

(3,719)

\newline

Choose

1

answer:

\newline

(A) The trending hashtag maintains

719

new social media posts per day for

3

days.

\newline

(B) The number of new social media posts associated with the trending hashtag increases by

719

per day for

3

days.

\newline

(C)

3

new social media posts associated with the trending hashtag are made

719

days after the hashtag's peak popularity.

\newline

(D)

719

new social media posts associated with the trending hashtag are made

3

days after the hashtag's peak popularity.

Plug in x value: Plug in the value of $x$ from the ordered pair $(3,719)$ into the function to check if it gives us $719$ . $\newline$ $f(3) = 2,500(0.66)^3$
Calculate power result: Calculate the value of $0.66$ raised to the power of $3$ . $\newline$ $(0.66)^3 = 0.287496$
Multiply by $2$ , $500$ : Multiply the result by $2,500$ to find $f(3)$ . $\newline$ $f(3) = 2,500 \times 0.287496$
Perform multiplication: Perform the multiplication to find the value of $f(3)$ . $f(3) = 719$
Interpret the result: Compare the result with the ordered pair $(3,719)$ to interpret its meaning. $\newline$ Since $f(3) = 719$ , the ordered pair means that $719$ new social media posts associated with the trending hashtag are made $3$ days after the hashtag's peak popularity.