   Chapter 5.5, Problem 6CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Checkpoint 6 Worked-out solution available at LarsonAppliedCalculus.com C 2 = 2.04 t + 4.7 ,  20 ≤ t ≤ 32 The projected fuel cost C (in millions of dollars per year) for a trucking company from 2020 to 2032 is where t = 20 corresponds to 2020. After purchasing more efficient truck engines, the company expects fuel costs to follow the model C 2 = 2.04 t + 4.7 ,  20 ≤ t ≤ 32 ,How much money will the company save with the more efficient engines?

To determine

To calculate: The money saved by the company with the more efficient engines if the projected fuel cost C (in millions of dollars per year) for a trucking company from 2020 to 2032 is modelled by the function,

C1=2.21t+5.6,20t32,C2=2.04t+4.7,20t32.

Explanation

Given Information:

The projected fuel cost C (in millions of dollars per year) for a trucking company from 2020 to 2032 is modelled by the function,

C1=2.21t+5.6,20t32

Here, t=20 corresponds to 2020.

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

C2=2.04t+4.7,20t32

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

The power rule is xndx=xn+1n+1+C,n1.

Calculation:

Consider the provided function C1=2.21t+5.6,20t32

And C2=2.04t+4.7,20t32

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

Sketch the graph of two functions as follows:

From the graph, C2C1 for all t in the interval [20,32]

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