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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Fuel Cost The projected fuel cost C (in millions of dollars) for an airline from 2020 through 2030 is

C 1 =   568.5   +   7.15 t where t = 20 corresponds to 2020. After purchasing more efficient airplane engines, the fuel cost is expected to decrease and to follow the model

C 2 =   525.6   +   6.43 t .

How much money will the airline save with the more efficient engines? Explain your reasoning.

To determine

To calculate: The money saved by the airline with the more efficient engines, if the projected fuel cost modelled by the function C1=568.5+7.15t is expected to decrease and follow the model C2=525.6+6.43t after purchasing more efficient airplane engines.

Explanation

Given Information:

The projected fuel cost C (in millions of dollars per year) for an airline from 2020 to 2030 is modeled by the function

C1=568.5+7.15t

Here, t=20 corresponds to 2020.

After purchasing more efficient truck engines, the fuel cost modeled by the function

C2=525.6+6.43t

Formula used:

Area of a region bounded by two graphs is calculated using the following formula,

If f and g are continuous on [a,b] and g(x)f(x) for all x in [a,b], then the area of the region bounded by the graphs of f, g, x=a and x=b is given by

A=ab[f(x)g(x)]dx

Calculation:

The money saved by the airlines with the more efficient engines will be represented as the area of the region between the graphs of C1 and C2.

As C2C1 for all t in the interval [20,30], the money saved will be,

Money saved=2030[C1C2]dt=2030[(568

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