Question

The first super bowl was played in 1967. The cost for a 30 second commercial was $42,000. The cost of a 30 second commercial for super bowl 52, which was played on February 4, 2018 in Minneapolis, Minnesota, was $5.0 million. What was the geometric mean rate of increase for the 51-year period? (Round your answer to 2 decimal places.)

Answer 1

It is given that the commercial rate for 1967 was 42000

The rate in 2018 was 5 million that means 5000000.

The number of years is given by:

`2018-1967=51`

So the formula for the geometric progression is given by:

`a_n=a_1r^(n-1)`

Substitute:

`a_n=5000000,a_1=42000,n=51`

To get:

`\begin{gathered} 5000000=42000r^(50) \\ r^(50)=(2500)/(21) \\ r=\sqrt[50]{(2500)/(21)} \\ r=1.100308364 \\ r\approx1.10 \end{gathered}`

Hence the rate is approximately 1.10.