The table gives the price t, in dollars, of a round-trip flight from Denver to Chicago on a certain airline and the corresponding monthly profit P for that airline on that route.Round-trip AirfaresProfit (thousandsdollars)Ticket Price(dollars)200308025035203003760350382040037004503380(a) Find a quadratic model for the data. (Round all numerical values to three decimal places.)P(t) =(b) Use the model to calculate the average rate of change of profit when the ticket price rises from $200 to $250. (Round your answer to three decimal places.)thousand dollars per dollar8.879(c) Use the model to calculate the average rate of change of profit when the ticket price rises from $350 to $400. (Round your answer to three decimal places.)2.221Xthousand dollars per dollar

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Asked Sep 26, 2019
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The table gives the price t, in dollars, of a round-trip flight from Denver to Chicago on a certain airline and the corresponding monthly profit P for that airline on that route.
Round-trip Airfares
Profit (thousands
dollars)
Ticket Price
(dollars)
200
3080
250
3520
300
3760
350
3820
400
3700
450
3380
(a) Find a quadratic model for the data. (Round all numerical values to three decimal places.)
P(t) =
(b) Use the model to calculate the average rate of change of profit when the ticket price rises from $200 to $250. (Round your answer to three decimal places.)
thousand dollars per dollar
8.879
(c) Use the model to calculate the average rate of change of profit when the ticket price rises from $350 to $400. (Round your answer to three decimal places.)
2.221
Xthousand dollars per dollar
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The table gives the price t, in dollars, of a round-trip flight from Denver to Chicago on a certain airline and the corresponding monthly profit P for that airline on that route. Round-trip Airfares Profit (thousands dollars) Ticket Price (dollars) 200 3080 250 3520 300 3760 350 3820 400 3700 450 3380 (a) Find a quadratic model for the data. (Round all numerical values to three decimal places.) P(t) = (b) Use the model to calculate the average rate of change of profit when the ticket price rises from $200 to $250. (Round your answer to three decimal places.) thousand dollars per dollar 8.879 (c) Use the model to calculate the average rate of change of profit when the ticket price rises from $350 to $400. (Round your answer to three decimal places.) 2.221 Xthousand dollars per dollar

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Expert Answer

Step 1

Use spreedsheet and compute the quadratic model for the given date as follows.

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B C E E G J K 1 200 3080 2 250 3520 3 300 3760 Chart Title 350 3820 4 4500 5 400 3700 4000 3380 6 450 3500 7 ttnsi 8 3000 9 2500 10 2000 11 y=-0.0374x2+ 25.529x - 527.14 1500 12 1000 13 500 14 0 15 100 200 300 400 500 16 17 18 From the above Figure, it is observed that the required quadratic model for the given date is P(t 0.0374x225.529x- 527.14 If all the numerical values rounded to three decimal places, then the quadratic model becomes P(t = -0.037x2 +25.529x -527.114 LL

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Step 2

(b) Compute the average rate of change of profit wh...

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P(250) P(200 3520-3080 250 200 50 440 50 =8.8 Thus, the average rate of change of profit when the ticket price rises from $200 to $250 is 8.8thousand dollars per dollar

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