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)200308025035203760300350382040037004503380(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.)-142.771X thousand dollars per dollar(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.)

Question
Asked Sep 26, 2019
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
3760
300
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.)
-142.771
X thousand dollars per dollar
(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.)
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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 3760 300 350 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.) -142.771 X thousand dollars per dollar (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.)

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Expert Answer

Step 1

To fit a quadratic function for the given data

Step 2

The idea is to choose constants A , B and C such that P(t) = A+Bt+Ct^2 best approximates the given data (sum of the squares of errors is minimum for this choice of A, B and C)

Step 3

(a) Using a suitable online quadratic regression calculator with ...

PC=-527.143+25.529t-0.0374
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PC=-527.143+25.529t-0.0374

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Math

Calculus

Functions