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

Answer:

The  revenue is $R(9) = \ 876.9$

Step-by-step explanation:

From the question we are told that

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

   $\frac{d R }{dt } = 13.897t + \frac{284.653}{t}$

Now  

     $dR = (13.897t + \frac{284.653}{t})dt$

Integrating both sides to obtain R(t)

     $\int\limits dR = \int\limits (13.897t + \frac{284.653}{t})dt$

    $\int\limits dR = \int\limits (13.897\frac{t^2}{2} + 284.653(ln (t)) ) + C$

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

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  

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

     $R(9) = \ 876.9$