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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.3, Problem 21QY
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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
19 views

The rate of change in revenue for Under Armour from 2004 through 2013 can be modeled by

d R d t = 35.38 t − 612.804 t where R is the revenue (in millions of dollars) and t is the time (in years), with t = 4 corresponding to 2004. In 2004, the revenue for Under Armour was $205.2 million. (Source: Under Armour, Inc.)

(a) Find a model for the revenue of Under Armour.

(b) Find the revenue of Under Armour in 2010.

(a)

To determine

To calculate: The model function for the revenue (in millions of dollars) of under Armour that rate of change in revenue for Under Armour from 2004 through 2013 can be model as:

dRdt=35.38t−612.804t

Explanation

Given Information:

The rate of change in revenue for Under Armour from 2004 through 2013 can be model as:

dRdt=35.38t−612.804t

Formula used:

The power rule of integrals:

∫undu=un+1n+1+C (for n≠1)

Here, u is function of x.

The property of Intro-differential:

∫df(x)dxdx=f(x)

Calculation:

The rate of change in revenue for Under Amour from 2004 through 2013 can be modeled by

dRdt=35.38t−612.804t

Integrate both side with respect to t.

∫dRdtdt=∫(35.38t−612.804t)dtR(t)=∫(35.38t−612.804t)dt

Now apply power and logarithmic rule of integration:

∫(35

(b)

To determine

To calculate: The revenue of Under Amour in 2010.

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