Math 10772700 Modeling Algebra PlusSpr Homework Hw 24b Expon

Math 10772-700 Modeling Algebra Plus-Spr Homework: Hw 24b. Exponential Equations Score: 0 of 1 pt 9 of 12 (12 complete) X Bus Econ 5.3.47 A minute ad ng a campaign in 1973 cost $200,000. The price tag for a 30-second ad slot during the 2002 campaign was s3 million. The cost of a 30-sec years after 1900 and y is the cost in millions. Complete (a-(b) a) According to the model, what was the cost of a 30-second campaign ad in 2005? The cost of a 30-second campaign ad in 2005 was 4,168,958 (Simplify your answer Round to the nearest dollar as needed) b) If the model remained accurate, when would the cost for a 30-second ad be $7.000,000? The model estimates the cost for a 30-second ad to be s7.000,000 in the year (Round up to the nearest year)

Solution

Given that cost of 30 second slt of advertising the campaign is modeled as y=0.0000965(1.107^x) where x is number of years after 1990 and y is cost in millions

A) cost of 30 second campaign in 2005 ,x=2005-1990=15 yrs.

plugging the value of x into the equation y=0.0000965(1.107^15) =4,433,448 dollars(rounded)

B) Given that the second campaign costs 7,000,000 dollars equating y=0.00000965(1.107^x)=7,000,000 dollars

apply log on both the sides log (1400/193)=x*log(1.107)

This on calculating gives x=19.49 years after the year 1990

So,its approximately in the year 2009