SOLUTION: Super Bowl Advertising: The average cost of 30 seconds of advertising during the Super Bowl 5 years ago was $2.2 million. If the increase in cost over the last 5 years has been 9%,

Question 73248: Super Bowl Advertising: The average cost of 30 seconds of advertising during the Super Bowl 5 years ago was $2.2 million. If the increase in cost over the last 5 years has been 9%, find the average cost of 30 seconds of advertising during the Super Bowl this year. Round to the nearest tenth of a million.
I times $2.2 million by .09 and it equaled 180,000. Next I added this to 2.2 million to get $2,180,000.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You have a couple of minor mistakes in your work. The problem says that the cost was $2.2 million
and at some point you appear to have switched to $2.0 million. As a result the 9% increase you
show is $180,000. The 9% increase for the first year should have been $198,000. So at the
end of the first year, the cost for an ad would have been $2,200,000 + $198,000 which equals
$2,398,000. But that is only the price after the first year. You still have to find the
increases for four more years. For the second year you will need to determine how much the price
will increase based on the last year's cost of $2,398,000 and the same 9% increase. And
on and on until you have done the same problem 5 times with a little different numbers each
time.
.
There is a little easier way to do this than work the same problem over and over.
Think about this ... each year the new price is 1.09 times the previous years price. Call
the baseline price P. (For this problem P will be $2.2 million). Then at the end of year 1 the
price will be P*1.09.
.
At the end of year 2 the price will go up again by a factor of 1.09 times the preceding year's
price. So it will be (P*1.09)*1.09 and this will be P*(1.09^2).
.
At the end of year 3 the price will go up again by a factor of 1.09 times the preceding year's
price. So it will be P*(1.09^2*1.09 and this will be P*(1.09^3).
.
You can go through this process two more times to find out that the final cost at the end
of the five years is given by the equation that says:
.
Final Price = P*(1.09^5)
.
For P substitute $2.2 million and the equation becomes:
.
Final Price = $2.2 million*(1.09^5)
.
Your calculator can be used to raise 1.09 to the 5th power (or you can multiply it out as:
.
1.09*1.09*1.09*1.09*1.09 = 1.538623955
.
This makes the Final Cost equation become:
.
Final Cost = $2.2 million * 1.538623955 = $3.38497270 or $3,384,972.70
.
Quite an increase. I hope this helps you to see your way through the problem and gives
you an appreciation for just what an annual 9% rate of inflation does to the cost of things.
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