Question 512047: I am so confused about my MAT 117 Appendix F. Can someone help me, any help would be appreciated.
Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. (x=1 is the day tickets go on sale).
Tickets=-0.2x^2+12x+11
a. Does the graph of this equation open up or down? How did you determine this?
b. Describe what happens to the tickets sales as time passes.
c. Use the quadratic equation to determine the last day that tickets will be sold.
Note. Write your answer in terms of the number of days after ticket sales begin.
d. Will tickets peak or be at a low during the middle of the sale? How do you know?
e. After how many days will the peak or low occur?
f. How many tickets will be sold on the day when the peak or low occurs?
g. What is the point of the vertex? How does this number relate to your answers in parts e. and f?
h. How many solutions are there to the equation ? How do you know?
i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).
Tickets: E(x) = -0.2x^2+12x+11
a. Does the graph of this equation open up or down?
Ans: down because the coefficient of the highest power term is negative.
How did you determine this?
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b. Describe what happens to the tickets sales as time passes?
Number of ticket sales goesup then down to zero.
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c. Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days after ticket sales begin.)
Solve E(x) = 0 for "x>0".
x = [-12 +- sqrt(144-4*-0.2*11)]/(-0.4)
x = [-12 +- sqrt(152.8)]/(-0.4)
Positive solution:
x = [-12-12.36]/-0.4
x = 60.9 days
On the 61st day, the ticket sales go to zero.
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d. Will tickets peak or be at a low during the middle of the sale? How do you know?
Ans: Peak; the parabola has a maximum point.
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e. After how many days will the peak or low occur?
30 th day
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f. How many tickets will be sold on the day when the peak or low occurs?
E(30) = 191
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g. What is the point of the vertex? (30,191)
(How does this number relate to your answers in parts e and f?
h. How many solutions are there to the equation ?
2 because it is a quadratic.
How do you know?
i. What do the solutions represent?
The two days when ticket sales are zero.
Is there a solution that does not make sense?
Yes: x = -0.90
If so, in what ways does the solution not make sense?
-0.90 is one day before sales began.
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Cheers,
Stan H.
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