Question

After having been on the air for more than a decade, Fox's American Idol seemed to be suffering from viewer fatigue. The average number of viewers from the 2011 season through the 2013 season is approximated by f(t) = 32.744e−0.252t (1 ≤ t ≤ 4) where f(t) is measured in millions, with t = 1 corresponding to the 2011 season.(a) What was the average number of viewers in the 2011 season? million viewers (b) What was the average number of viewers in the 2014 season, assuming that the trend continued into that season? million viewers

Answer 1

(a)25.45 million viewers

(b) 11.95 million viewers

Explanation:

The average number of viewers from the 2011 season through the 2013 season is approximated by the function:

[Tex] f(t) = 32.744*e^{-0.252t}[/tex] (1 ≤ t ≤ 4) where f(t) is measured in millions.

t = 1 corresponds to the 2011 season.

(a) In 2011, t=1

Average number of viewers in the 2011 season,

[Tex] f(1) = 32.744*e^{-0.252*1}[/tex]

=25.45 million viewers

(b) In the 2014 season, when =4

[Tex] f(4) = 32.744*e^{-0.252*4}[/tex]

=11.95 million viewers

assuming that the trend continued into that season