Question 425729: Use an Equation Editor to write mathematical expressions and equations.
Ticket Sales
Living in or near a metropolitan area has some advantages. Entertainment opportunities are almost endless in a major city. Events occur almost every night, from sporting events to the symphony. Tickets to these events are not available long and can often be modeled by quadratic equations.
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. ( is the day tickets go on sale).
Tickets = -0.26x^2+13x+35
1. Does the graph of this equation open up or down? How did you determine this?
2. Describe what happens to the tickets sales as time passes?
3. Will tickets peak or be at a low during the middle of the sale? How do you know?
4. How many solutions are there to the equation ? How do you know?
5. Use the quadratic equation to determine the last day that tickets will be sold
Write your answer in terms of the number of days after ticket sales begin.
(Note: that we do not use partial days or negative sales)
So day will be the last day.
6. 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?
7. Determine the number of tickets sold on the 52 day
8. Determine the number of tickets sold on the 1st day
9. After how many days will the peak or low occur?
Using
10. How many tickets will be sold on the day when the peak or low occurs?
Substitute x = ? into original model:
tickets are sold on the busiest day.
11. How many tickets will be sold on day 26
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! I understand that all the problems are correlated, but this is too many problems on one post. I am quite sure you can knock off half of these problems without much thought (for example, #7, 8, 11, as well as #1-3). #4 and #5 both involving using the quadratic formula, which you should know, then #6 should immediately follow. Also, to find the peak or low, note that the vertex occurs at -b/2a, or -(-13)/(2*-0.26). That should get you through all the problems.
|
|
|
