a magician performs in a hall that has a seating capacity of 1,000 spectators. with ticket prices set at…

a magician performs in a hall that has a seating capacity of 1,000 spectators. with ticket prices set at $47, average attendance has been 640 spectators. a marketing survey shows that for each dollar the ticket price is lowered, the average attendance increases by 20. write a function that models the revenue in terms of ticket price.\n\na. f(x)=(47 + x)(20 - 640x)\nb. f(x)=(47 - x)(640 + 20x)\nc. f(x)=(47x - 1)(640 - 20x)\nd. f(x)=(640 - x)(47 + 20x)

a magician performs in a hall that has a seating capacity of 1,000 spectators. with ticket prices set at $47, average attendance has been 640 spectators. a marketing survey shows that for each dollar the ticket price is lowered, the average attendance increases by 20. write a function that models the revenue in terms of ticket price.\n\na. f(x)=(47 + x)(20 - 640x)\nb. f(x)=(47 - x)(640 + 20x)\nc. f(x)=(47x - 1)(640 - 20x)\nd. f(x)=(640 - x)(47 + 20x)

Answer

Explanation:

Step1: Define the variables

Let $x$ be the number of dollars the ticket - price is lowered. The new ticket price is $p = 47 - x$.

Step2: Define the number of attendees

The initial average attendance is 640, and for each dollar the ticket price is lowered, the attendance increases by 20. So the number of attendees $n=640 + 20x$.

Step3: Recall the revenue formula

Revenue $R$ is the product of the ticket price and the number of attendees, i.e., $R=p\times n$.

Step4: Substitute the expressions for $p$ and $n$

Substitute $p = 47 - x$ and $n = 640+20x$ into the revenue formula. We get $R=(47 - x)(640 + 20x)$. So the function that models the revenue in terms of the ticket price is $f(x)=(47 - x)(640+20x)$.

Answer:

B. $f(x)=(47 - x)(640+20x)$