The rate of change in revenue for Under Armour from 2004 through 2009 can be mod

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

Explanation / Answer

dR/dt = 13.897t + 284.653/t

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

Integrating on both sides

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

==> R(t) = 13.897(t2/2) + 284.653(ln t) + c       since xn dx = xn+1/(n +1) ; 1/x dx = lnx + c

==> R(t) = 6.9485t2 + 284.653(ln t) + c

Given that at t = 8 , R(8) = $725.2 million

==> 725.2 = 6.9485(8)2 + 284.653(ln 8) + c

==> c = -311.42327

==> c = -311.42

Hence R(t) = 6.9485t2 + 284.653(ln t) - 311.42

b) t = 9 ==> year 2009

==> R(9) = 6.9485(9)2 + 284.653(ln 9) - 311.42

==> R(9) = 876.855

Hence revenue in 2009 is $876.86 million

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