   Chapter 5.5, Problem 49E ### 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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# Revenue In Exercises 49 and 50, two models, R1 and R2, are given for revenue (in billions of dollars) for a large corporation. Both models are estimates of revenues for 2020 through 2025, where t = 20 corresponds to 2020. Which model projects the greater revenue? How much more total revenue does that model project over the six-year period? R 1 = 7.21 + 0.58 t ,   R 2 = 7.21 + 0.45 t

To determine

To calculate: The model which projects the greater revenue projects the greater revenue from two models of revenue R1=7.21+0.58t and R2=7.21+0.45t. Also, the amount of more revenue that model project over the six-year period.

Explanation

Given Information:

Two models for revenue (in billions of dollars) for a large corporation are given as,

R1=7.21+0.58t and R2=7.21+0.45t

Two models are estimates of revenues for 2020 through 2025, where t=20 corresponds to 2020.

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:

Consider two revenue functions,

R1=7.21+0.58t and R2=7.21+0.45t

Consider the first function R1=7.21+0.58t

It is a linear function. So, its graph will be a straight line with slope m=0.58 and y-intercept b=7.21.

Consider the second function R2=7.21+0.45t

It is a linear function. So, its graph will be a straight line with slope m=0.45 and y-intercept b=7.21.

Compute the points of intersection of two graphs by setting the functions equal to each other and solving for x,

7.21+0.58t=7.21+0.45t0.58t0.45t=0t=0

Substitute t=0 in the function R2=7.21+0.45t and compute the intersection point,

R2=7.21+0.45×0=7

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