Question
The price of a ticket at a theater is xx dollars. The manager of the the theater uses the function f, of, x, equals, minus, 4, x, squared, plus, 100, xf(x)=−4x
2
+100x to predict f, of, xf(x) , the total ticket sales in dollars.
Part A:
What are the predicted total sales, in dollars, when the price of a ticket is 9 dollars? Show or explain how you got your answer.
Enter your answer and your work or explanation in the space provided.
Answer
2
+100x to predict f, of, xf(x) , the total ticket sales in dollars.
Part A:
What are the predicted total sales, in dollars, when the price of a ticket is 9 dollars? Show or explain how you got your answer.
Enter your answer and your work or explanation in the space provided.
Answer
Answers
Answered by
GPT-4o mini
To find the predicted total sales when the price of a ticket is 9 dollars using the function \( f(x) = -4x^2 + 100x \), we will substitute \( x = 9 \) into the function.
1. Substitute \( x = 9 \) into the function:
\[
f(9) = -4(9)^2 + 100(9)
\]
2. Calculate \( (9)^2 \):
\[
(9)^2 = 81
\]
3. Substitute this value into the equation:
\[
f(9) = -4(81) + 100(9)
\]
4. Now compute \( -4(81) \):
\[
-4(81) = -324
\]
5. Compute \( 100(9) \):
\[
100(9) = 900
\]
6. Combine the results:
\[
f(9) = -324 + 900
\]
\[
f(9) = 576
\]
The predicted total sales when the price of a ticket is 9 dollars is **576 dollars**.
1. Substitute \( x = 9 \) into the function:
\[
f(9) = -4(9)^2 + 100(9)
\]
2. Calculate \( (9)^2 \):
\[
(9)^2 = 81
\]
3. Substitute this value into the equation:
\[
f(9) = -4(81) + 100(9)
\]
4. Now compute \( -4(81) \):
\[
-4(81) = -324
\]
5. Compute \( 100(9) \):
\[
100(9) = 900
\]
6. Combine the results:
\[
f(9) = -324 + 900
\]
\[
f(9) = 576
\]
The predicted total sales when the price of a ticket is 9 dollars is **576 dollars**.