document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #52475 by bucky(2189)\"\" \"About 
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You have a couple of minor mistakes in your work. The problem says that the cost was $2.2 million
\n" ); document.write( "and at some point you appear to have switched to $2.0 million. As a result the 9% increase you
\n" ); document.write( "show is $180,000. The 9% increase for the first year should have been $198,000. So at the
\n" ); document.write( "end of the first year, the cost for an ad would have been $2,200,000 + $198,000 which equals
\n" ); document.write( "$2,398,000. But that is only the price after the first year. You still have to find the
\n" ); document.write( "increases for four more years. For the second year you will need to determine how much the price
\n" ); document.write( "will increase based on the last year's cost of $2,398,000 and the same 9% increase. And
\n" ); document.write( "on and on until you have done the same problem 5 times with a little different numbers each
\n" ); document.write( "time.
\n" ); document.write( ".
\n" ); document.write( "There is a little easier way to do this than work the same problem over and over.
\n" ); document.write( "Think about this ... each year the new price is 1.09 times the previous years price. Call
\n" ); document.write( "the baseline price P. (For this problem P will be $2.2 million). Then at the end of year 1 the
\n" ); document.write( "price will be P*1.09.
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\n" ); document.write( "At the end of year 2 the price will go up again by a factor of 1.09 times the preceding year's
\n" ); document.write( "price. So it will be (P*1.09)*1.09 and this will be P*(1.09^2).
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\n" ); document.write( "At the end of year 3 the price will go up again by a factor of 1.09 times the preceding year's
\n" ); document.write( "price. So it will be P*(1.09^2*1.09 and this will be P*(1.09^3).
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\n" ); document.write( "You can go through this process two more times to find out that the final cost at the end
\n" ); document.write( "of the five years is given by the equation that says:
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\n" ); document.write( "Final Price = P*(1.09^5)
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\n" ); document.write( "For P substitute $2.2 million and the equation becomes:
\n" ); document.write( ".
\n" ); document.write( "Final Price = $2.2 million*(1.09^5)
\n" ); document.write( ".
\n" ); document.write( "Your calculator can be used to raise 1.09 to the 5th power (or you can multiply it out as:
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\n" ); document.write( "1.09*1.09*1.09*1.09*1.09 = 1.538623955
\n" ); document.write( ".
\n" ); document.write( "This makes the Final Cost equation become:
\n" ); document.write( ".
\n" ); document.write( "Final Cost = $2.2 million * 1.538623955 = $3.38497270 or $3,384,972.70
\n" ); document.write( ".
\n" ); document.write( "Quite an increase. I hope this helps you to see your way through the problem and gives
\n" ); document.write( "you an appreciation for just what an annual 9% rate of inflation does to the cost of things. \n" ); document.write( "
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