According to date from Nielson Media Research, the audiencefor the ABC nightly n

Question

According to date from Nielson Media Research, the audiencefor the ABC nightly news (in millions) can be approximated by -0.458x+15.375, where x=3corresponds to 1993. If this model remains accurate, in what years is the audiencebetween 6,673,000 and 8,505,000? According to date from Nielson Media Research, the audiencefor the ABC nightly news (in millions) can be approximated by -0.458x+15.375, where x=3corresponds to 1993. If this model remains accurate, in what years is the audiencebetween 6,673,000 and 8,505,000?

Explanation / Answer

Let's figure out when the audience is at 6.673 million, and whenthe audience is at 8.505 million. These will give the boundaryyears for when the audience is in that range. Using the formula given, we have: audience = -.458x + 15.375 So plugging in our desired audience values, we get: 6.673 = -.458x + 15.375 Subtracting 15.375 from both sides: -8.702 = -.458x Dividing both sides by -.458: x = 19 8.505 = -.458x + 15.375 Subtracting 15.375 from both sides: -6.87 = -.458x Dividing both sides by -.458: x = 15 Now x = 3 corresponds to 1993, so year = x + 1990. Therefore, they have 6.673 million viewers in the year 19 + 1990 =2009 And they have 8.505 million viewers in the year 15 + 1990 =2005 Therefore, they have between 6.673 and 8.505 million viewers from2005 to 2009.

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