The table gives the price, in dollars, of a round-trip ticket from Denver to Chicago on a certain airline and the corresponding monthly profit, in millions of dollars, for that airline. Profit from the sale of Round-Trip Tickets Ticket Price Profit (dollars) 200 250 300 350 400 450 . (million dollars) 2.64 2.92 2.99 2.86 2.52 1.98 (a) Explain why a quadratic model is more appropriate for the data than a log or exponential model. The data indicates a minimum point and changes from decreasing to increasing at that point. Logarithmic and exponential functions d not possess minimum points, but quadratic functions do. The data indicates a maximum and changes from increasing to decreasing at the point. Logarithmic and exponential functions do not possess maximum points but quadratic functions do. The data indicates the graph is only increasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. 4 The data indicates the graph is only decreasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. (b) Find a quadratic model for the data. (Round all numerical values to six decimal places.) P(x)= million dollars (c) Why doesn't the airline profit increase as the ticket price increases? The airline has to provide more amenities for passengers to justify the price increase.
The table gives the price, in dollars, of a round-trip ticket from Denver to Chicago on a certain airline and the corresponding monthly profit, in millions of dollars, for that airline. Profit from the sale of Round-Trip Tickets Ticket Price Profit (dollars) 200 250 300 350 400 450 . (million dollars) 2.64 2.92 2.99 2.86 2.52 1.98 (a) Explain why a quadratic model is more appropriate for the data than a log or exponential model. The data indicates a minimum point and changes from decreasing to increasing at that point. Logarithmic and exponential functions d not possess minimum points, but quadratic functions do. The data indicates a maximum and changes from increasing to decreasing at the point. Logarithmic and exponential functions do not possess maximum points but quadratic functions do. The data indicates the graph is only increasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. 4 The data indicates the graph is only decreasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. (b) Find a quadratic model for the data. (Round all numerical values to six decimal places.) P(x)= million dollars (c) Why doesn't the airline profit increase as the ticket price increases? The airline has to provide more amenities for passengers to justify the price increase.
Chapter3: Polynomial Functions
Section3.1: Quadratic Functions And Models
Problem 7E: In Exercises 5-8, match the quadratic function with its graph. [...
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Transcribed Image Text:The table gives the price, in dollars, of a round-trip ticket from Denver to Chicago on a certain airline and the corresponding monthly profit, in
millions of dollars, for that airline.
Profit from the sale of Round-Trip Tickets
Ticket Price
Profit
(dollars)
(million dollars)
200
250
300
350
400
450
.
2.64
2.92
2.99
2.86
2.52
1.98
(a) Explain why a quadratic model is more appropriate for the data than a log or exponential model.
The data indicates a minimum point and changes from decreasing to increasing at that point. Logarithmic and exponential functions do
not possess minimum points, but quadratic functions do.
The data indicates a maximum and changes from increasing to decreasing at the point. Logarithmic and exponential functions do not
possess maximum points but quadratic functions do.
The data indicates the graph is only increasing. Logarithmic and exponential functions both increase and decrease while quadratic
functions either increase or decrease.
e
The data indicates the graph is only decreasing. Logarithmic and exponential functions both increase and decrease while quadratic
functions either increase or decrease.
(b) Find a quadratic model for the data. (Round all numerical values to six decimal places.)
P(x)=
million dollars
(c) Why doesn't the airline profit increase as the ticket price increases?
The airline has to provide more amenities for passengers to justify the price increase.
More taxes must be paid on the increased revenue.
As ticket prices increase, fewer tickets will be sold at the increased price leading to a decline in profit.
Crew members have their pay increased when ticket prices go up.
(d) Report the ticket price (to the nearest dollar) at which the airline will begin to post a negative profit (that is, a net loss).
dollars
X=
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