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The number of TV channels that the average U.S. home receives has been soaring in recent, years. The function $t(x)=0.16 x^{2}+0.46 x+21.36$can be used to estimate ...

Question

The number of TV channels that the average U.S. home receives has been soaring in recent, years. The function $t(x)=0.16 x^{2}+0.46 x+21.36$can be used to estimate this number, where $x$ is the number of years after 1985 (Source: Nielsen Media Research, National People Meter Sample). Use this func-tion for Exercises 97 and 98.In what year did the average U.S. household receive50 channels?

The number of TV channels that the average U.S. home receives has been soaring in recent, years. The function $t(x)=0.16 x^{2}+0.46 x+21.36$can be used to estimate this number, where $x$ is the number of years after 1985 (Source: Nielsen Media Research, National People Meter Sample). Use this func-tion for Exercises 97 and 98. In what year did the average U.S. household receive 50 channels?



Answers

The number of TV channels that the average U.S. home receives has been soaring in recent, years. The function $t(x)=0.16 x^{2}+0.46 x+21.36$can be used to estimate this number, where $x$ is the number of years after 1985 (Source: Nielsen Media Research, National People Meter Sample). Use this func-tion for Exercises 97 and 98. In what year did the average U.S. household receive 50 channels?

It is even that the table show the percentage off US houses with cable TV. We need to find the quadratic model using 96 as l 0 90 70 1970 as year 10 and so on. Now. By using this, our table reduces to reduces as here, percentage off household introduces two in zero ear, the percentage is 0% and after 10 years the percentage is 7%. And after 20 years the percentages 20%. And after 30 years, the percentages 56 after 40 years, the percentage is 68%. Now, by using this information and by considering the standard quality model system, we have a access to power two plus B X plus e is equal to FX. Now. We're putting X is equal to zero, and F X is equal to zero. We have the value off C is equal to zero now by putting X is equal to 10 and affects physical to seven. We have the incubation 100. A plus 10 B plus C is equal to seven now. Putting the value of C is equal to zero. We have 100 A plus. 10 B is equal to seven called Dedication one. Now we're putting X is equal to 20 and FX is equal to 20. We have 400. A plus 20 plus C is equal to 20. Now we're putting The value of C is equal to zero. The equation will reduces to 400. A plus 20 b is equal to 20 which is equal toe 20 a plus B is equal to one now by multiplying the equation with again and then by simplifying the question one and two. We have the 200 A plus 10 b is equal to 10 100 a plus. 10 b is equal to seven now by changing the sign off the second equation, we have the Valley off a is equal toe three upon 100. Now we're putting the value off a immigration second we have the value of B is equal to four upon 10. So off a system is equal to the quantity equation. FX is equal to three upon 100 extras to power to plus four upon 10. Now we need to find a percentage of the household in the 1995 year. Now, by putting the X is equal toe 35 we have the value off. F off 35 is equal to 37.15% it So this is our answer.

All right. Just gonna do the part divided by the whole thing. Okay, so we've got, um, 62.0 1,000,000 people that owned three or more TV. So at least three TVs and then we've got 100 and 14.9 million that own at least one. So the percent of the people that own at least three out of the out of the total that own at least one will be 62 divided by 1 14.9 Go to our calculator. And that's, um what do we get around to? We'll go to one decimal place. So it's about 10.5395 So what, 54.0%?

All right. So we've got, um, 88% right. That is a decimal 0.8, um, the received basic cable. And this is out of all the people that have at least one TV in their household. So that's 114.9 million people. So if we do, the number of households that have cable divided by the total number that have a TV will end up with the percent 88 that ah, have cable and a TV. All right, So multiply both sides of this equation by 1 14.9 and we'll have our answer. So 0.88 times 1 14.9 that's Ah, 101 were in around this a little bit. 1010.11 twos will make it point one 1,000,000 people are 1,000,000 households

All right. So we've got 35% of households that receive premium cable. Of the, uh, people are the households that have at least one. How are one TV is so, um, if we do not basic cable, this is the number that have premium cable over the number that have a TV and a 35%. So if we just multiply both sides of this but 1 14.9 then we'll know the number of households that get premium cable. What he dogs. All right, So 1 14.9 times 0.35 is 40.215 So we'll call 40 0.2 million.


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