Question 134658: Here are the percentages of households with cable TV for certain years
Year 1976 1977 1978 1979 1980
Percentage with cable TV 15.1 16.6 17.9 19.4 22.6
Use exponential regression to construct an exponential model for the original cable TV data.
Based on your formula in part a, what was the yearly percentage growth in percentage of households with cable TV?
According to your formula, what percentage of households are predicted to have cable TV by the year 2003? Is this a reasonable answer?
Plot the natural logarithm of the data points.
Explain why your plot in part (d) shows that the original data is close to exponential.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Here are the percentages of households with cable TV for certain years
Year 1976 1977 1978 1979 1980
Percentage with cable TV 15.1 16.6 17.9 19.4 22.6
Use exponential regression to construct an exponential model for the original cable TV data.
I limited the coefficients to 4 decimal places and got:
Percentage = 0.01*1.1010^x where x is # of years after 1976.
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Based on your formula in part a, what was the yearly percentage growth in percentage of households with cable TV?
At year x=0, Percent = 0.01*1 = 1%
At year x=1 Percent = 0.01*1.1010 = 0.011 = 1.1%
The growth is 0.1%
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According to your formula, what percentage of households are predicted to have cable TV by the year 2003? Is this a reasonable answer?
2003 is 27 years after 1976
Percent(in 2003) = 0.01*1.1010^27 = 0.1344 = 13.44%
It probably should be higher.
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Plot the natural logarithm of the data points.
2.7147 ; 2.8094 ; 2.8848 ; 2.9653 ; 3.1179
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Explain why your plot in part (d) shows that the original data is close to exponential.
Not sure what that is all about.
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Cheers,
Stan H.
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