TV Viewers: Newsmagazine Shows The number of viewers of a weekly TV newsmagazine show, introduced in the 2009 season, has been increasing at the rate of...

Question

2(3 + 1/2t)^-1/3 (1 ≤ t ≤ 6)

million viewers/year in its t th year on the air where t = 1 corresponds to 2009. The number of viewers of the program during its first year on the air is given by 6(7/2)^2/3 million. Find how many viewers were expected in the 2012 season. (Round your answer to one decimal place.)

_____ million viewers

Answer 1

r(t)=2(3+t/2)^-1/3

Let v(t) be the million number of viewers

v(t) =∫r(t)dt=∫2(3+t/2)^-1/3dt

Let u = 3+t/2 du=dt/2

when t = 1, u = 7/2

when t = 4, u = 5

v(u) =4∫u^-1/3du = 4(3/2)u^2/3 + C

v(7/2) = 6(7/2)^2/3 + C = 6(7/2)^2/3 ==> C=0

v(5) = 6(5)^2/3 ≈ 17.5 million viewers