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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem

Revenue The rate of change in revenue for DIRECTV from 2004 through 2013 can be modeled by

d R d t = 3.17 6.671 t where R is the revenue (in billions of dollars) and t is the time (in years), with t = 4 corresponding to 2004. In 2010, the revenue for DIRECTV was $24.1 billion. (Source: DIRECTV)

(a) Find a model for the revenue of DIRECTV.

(b) Find the revenue of DIRECTV in 2013.

(a)

To determine

To calculate: A model function for the revenue of DIRECTV from 2004 through 2013 that rate of change given by dRdt=3.176.671t.

Explanation

Given Information:

The rate of change of revenue function,

dRdt=3.176.671t

When t=4year, the revenue (in billions of dollars) of DIRECTV is $24.1billion.

Where time (in days) is t and R is the revenue (in billions of dollars).

Formula used:

The exponent rule of integrals:

eu(x)du(x)=eu(x)+C

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

The logarithmic rule of integration:

dtt=ln|t|+C

Calculation:

Consider the rate of change of revenue function,

dRdt=3.176.671t

Integrate both sides with respect to t,

dRdtdt=(3

(b)

To determine

To calculate: The revenue of DIRECTV in 2013.

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