   Chapter 5.5, Problem 50E ### 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 + 0.26 t + 0.02 t 2 ,   R 2 = 7.21 + 0.1 t + 0.01 t 2

To determine

To calculate: The model which projects the greater revenue from two models of revenue R1=7.21+0.26t+0.02t2 and, R2=7.21+0.1t+0.01t2 and 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+0.26t+0.02t2 and R2=7.21+0.1t+0.01t2

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+0.26t+0.02t2 and R2=7.21+0.1t+0.01t2

Consider the first function R1=7.21+0.26t+0.02t2

It is a quadratic function. So, its graph will be a parabola with opening upwards. For the interval [20,25], the revenue will be positive. Compute its y-intercept,

R1=7.21+0.26×0+0.02×02=7.21

So, the graph intersects the revenue axis at R=7.21.

Consider the second function R2=7.21+0.1t+0.01t2

It is a quadratic function. So, its graph will be a parabola with opening upwards. For the interval [20,25], the revenue will be positive. Compute its y-intercept,

R2=7.21+0.1×0+0.01×02=7.21

So, the graph intersects the revenue axis at R=7.21.

As two parabolas intersect the revenue axis at same point R=7.21, they will intersect at the point (0,7.21).

Now, sketch the graph of two functions as follows:

From the graph, R2R1 for all t in the interval [20,25]

Thus, model R1=7

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