Question

The cost, in millions of dollars, of a 30-second television ad during the Super Bowl in the years 2000 to 2010 can be approximated by

C(t)=0.14t+1.1 million dollars (0≤t≤10)
(t=0 represents 2000).+ What was the average cost (in millions of dollars) of a Super Bowl ad during the given period? (Round your answer to one decimal places.)
$__________ million

Answer 1

The average cost of a Super Bowl ad from 2000 to 2010 is 1.8 million dollars, calculated by integrating the cost function and dividing by the number of years.

Step-by-step explanation:

The formula given, C(t) = 0.14t + 1.1, represents the cost, in millions of dollars, of a 30-second television ad during the Super Bowl from the year 2000 to 2010, where t is the number of years after 2000. To find the average cost during this period, we integrate the function over the interval from t = 0 to t = 10 (the years 2000 to 2010), and then divide by the length of the interval (10 years).

The integral of C(t) from 0 to 10 is:

∫010 C(t) dt = ∫010 (0.14t + 1.1) dt = [0.07t2 + 1.1t] from 0 to 10 = (0.07(10)2 + 1.1(10)) - (0.07(0)2 + 1.1(0)) = 7 + 11 = 18 million dollars

Now, the average cost is the total cost divided by 10 years:

Average cost = Total cost / Number of years
= 18 million dollars / 10
= 1.8 million dollars (rounded to one decimal place).