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 AirfaresTicket PriceProfit (thousandsdollars)(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.)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.)thousand dollars per dollar

Question
Asked Sep 25, 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
Ticket Price
Profit (thousands
dollars)
(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.)
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.)
thousand 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 Ticket Price Profit (thousands dollars) (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.) 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.) thousand dollars per dollar

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check_circleExpert Solution
Step 1

Given information:

 

Step 2

Calculation:

a)

1. Press the Y= key and clear any equations.

2. Press the STAT key, use the arrow keys to select EDIT, and enter this data.

3. Press the STAT key, select CALC, and choose option number 5: QuadReg. This will bring you back to the home screen, with QuadReg showing. Type "L1, L2" by pressing 2nd and 1, then comma, then 2nd and 2. Type "Y1" by pressing VARS, moving across to Y-VARS, choosing Function, and choosing option number 1. Your home screen should show:

QuadReg L1, L2, Y1
QuadReg
y=ax2+bx+c
a=-.0374285714
b 25.52957143
C= -527.1428571
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QuadReg y=ax2+bx+c a=-.0374285714 b 25.52957143 C= -527.1428571

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Step 3

The quadratic m...

y0.374x25.529x-527.143
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y0.374x25.529x-527.143

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