Since YouTube first became available to the public in mid-2005, the rate at which video has been uploaded to the site can be approximated by
v(t) = 525,600(0.42t2 + 2.7t − 1) hours of video per year (0.5 ≤ t ≤ 7),
where t is time in years since the start of 2005.

a) Find an expression for the total number of hours
V(t) of video at time t
(starting from zero hours of video at t = 0.5)

b) Use the answer to part (a) to estimate the total number of hours of video uploaded by the start of 2012. (Round your answer to the nearest million hours of video.)

Question

Since YouTube first became available to the public in mid-2005, the rate at which video has been uploaded to the site can be approximated by
v(t) = 525,600(0.42t2 + 2.7t − 1) hours of video per year    (0.5 ≤ t ≤ 7),
where t is time in years since the start of 2005.

a) Find an expression for the total number of hours 
V(t) of video at time t
 (starting from zero hours of video at t = 0.5)

b) Use the answer to part (a) to estimate the total number of hours of video uploaded by the start of 2012. (Round your answer to the nearest million hours of video.)