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.† (Round your answers to three decimal places.) (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

Answer:

a) In the first season, there were 25.450 million viewers.

b) In the fourth season, the number of viewers was 11.950 million.

Step-by-step explanation:

Hi there!

The average number of viewers in season t is given by the following function:

$f(t) = 32.744 e^{-0.252t}$

a) To obtain the average number of viewers in season 1, we have to evaluate the function at t = 1:

$f(1) = 32.744e^{-0.252 (1)} = 25.450$

In the first season, there were 25.450 million viewers.

b) Now we have to evaluate the function at t = 4:

$f(4) = 32.744e^{-0.252(4)} = 11.950$

In the fourth season, the number of viewers was 11.950 million.