Question

The rate of change in revenue for Under Armour from 2004 through 2009 can be modeled by dR /dt = 13.897t + 284.653 t where R is the revenue (in millions of dollars) and t is the time (in years), with t = 4 corresponding to 2004. In 2008, the revenue for Under Armour was $725.2 million.

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(a) Find a model for the revenue of Under Armour. (Round your constant term to two decimal places.) R(t) = 6.9485t2+284.653 ln(t)-311.42 Correct: Your answer is correct.
(b) Find Under Armour's revenue in 2009. (Round your answer to two decimal places.) $ million

Answer 1

The revenue is
`R(9) = \$ 876.9`

Explanation:

From the question we are told that

The rate of change in revenue for Under Armour from 2004 through 2009 is

`(d R )/(dt ) = 13.897t + (284.653)/(t)`

Now

`dR = (13.897t + (284.653)/(t))dt`

Integrating both sides to obtain R(t)

`\int\limits dR = \int\limits (13.897t + (284.653)/(t))dt`

`\int\limits dR = \int\limits (13.897(t^2)/(2) + 284.653(ln (t)) ) + C`

=>
`R(t) = 6.9485t^2 + 284.653(ln (t) ) + C`

From the question we have that at t = 8
`R(8)= \$ 725.2 \ million`

`725.2 = 6.9485(8)^2 + 284.653(ln (8) ) + C`

=>
`C = -311.4`

So

`R(t) = 6.9485t^2 + 284.653(ln (t) ) -311.4`

At t = 9

`R(9) = 6.9485*(9)^2 + 284.653(ln (9) ) -311.4`

`R(9) = \$ 876.9`