Question 1131534: Hi, I was wondering how I would solve this question.
The average ticket price to see a Drive‐in movie between 1993 and 1998, is modelled by
𝐶 =0.025𝑥^2- 0.4𝑥 +8.25 where C is the cost of the ticket in dollars and 𝑥 is the number of years after 1993(x= 0 in 1993)
a) What will be the admission cost in 2017?
b) When will the admission cost be $20.00
I know that I have to solve for the vertex but I dont know what to do with the numbers after, thank you for your time.
Found 2 solutions by rothauserc, MathTherapy:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! a) 2017 - 1993 = 14
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C = 0.025(14^2) -0.4(14) +8.25 = 7.55
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The cost of an admission ticket in 2017 is $7.55
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b) 20 = 0.025x^2 -0.4x +8.25
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solve for x
:
0.025x^2 -0.4x -11.75 = 0
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divide both sides of = by 0.025
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x^2 -16x -470 = 0
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use quadratic formula to solve for x
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x = (-(-16) + square root( (-16)^2 -4 * 1 * (-470))/(2(1))) = 31.1
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x = (-(-16) - square root( (-16)^2 -4 * 1 * (-470))/(2(1))) = -15.1
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we reject the negative value for x
:
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The admission cost will be $20.00 in 31.1 years
:
check the answer
:
C = 0.025(31.1^2) -0.4(31.1) +8.25 = 19.99025 is approximately 20 years
:
answer checks
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Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website!
Hi, I was wondering how I would solve this question.
The average ticket price to see a Drive‐in movie between 1993 and 1998, is modelled by
𝐶 =0.025𝑥^2- 0.4𝑥 +8.25 where C is the cost of the ticket in dollars and 𝑥 is the number of years after 1993(x= 0 in 1993)
a) What will be the admission cost in 2017?
b) When will the admission cost be $20.00
I know that I have to solve for the vertex but I dont know what to do with the numbers after, thank you for your time.
No, you don't need to find the vertex, unless you're looking to find the year when the price will "max" out,
and also what cost represents that time.
Correct answers: 
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