Respuesta :
Answer:
[tex]f(t) = \int 0.82 t +1.14 dt[/tex]
[tex] f(t) = \frac{0.82}{2}t^2 +1.14 t +C[/tex]
Where C is a constant, now using the initial condition we got:
[tex] f(2)= 5.9 = 0.41 (2)^2 + 1.14*2 +C[/tex]
And solving for C we got:
[tex] C= 5.9 -0.41(4) -1.14*2 = 1.98[/tex]
And the function desired for the advertising revenue would be given by:
[tex]f(t) = 0.41t^2 1.14t +1.98 [/tex]
With f the amount in billions and the the years since 2002 to 2006.
Explanation:
For this case we have the following function who represent the revenue grew rate:
[tex] r(t) = 0.82t +1.14 , 0 \leq t \leq 4[/tex]
And we want to calculate the Advertising revenue so we need to integrate the function r(t) and we can use the inidital condition t=0 , f(2)= 5.9 billion.
If we integrate the function we got:
[tex]f(t) = \int 0.82 t +1.14 dt[/tex]
[tex] f(t) = \frac{0.82}{2}t^2 +1.14 t +C[/tex]
Where C is a constant, now using the initial condition we got:
[tex] f(2)= 5.9 = 0.41 (2)^2 + 1.14*2 +C[/tex]
And solving for C we got:
[tex] C= 5.9 -0.41(4) -1.14*2 = 1.98[/tex]
And the function desired for the advertising revenue would be given by:
[tex]f(t) = 0.41t^2 1.14t +1.98 [/tex]
With f the amount in billions and the the years since 2002 to 2006.
