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Question 941628: In 1995, there were 33.8 million cellular subscribers in the US. In 1999 there were 86 million.
a. Let x=5 represent 1995 and e=9 represent 1999. Find the average rate of change in the number of subscribers in the US.
b. Write a linear function that models the number of cellular subscribers in the US
c. Interpret the average rate of change and the y-intercept using a complete sentence and be specific to this problem.
d. According to the calculations, how many cellular subscribers will there be in 2012?
e. Is this a good estimation? Why or why not?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! a:
rate = dy/dx
rate = (86 - 33.8)/(9 - 5)
rate = 13.05 million/year
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b:
y - 86 = 13.05(x - 9)
y - 86 = 13.05x - 13.05*9
y = 13.05x + 86 - 13.05*9
y = 13.05x - 31.45
f(x) = 13.05x - 31.45
where:
x = years since 1990
y = millions of mobile subscribers in the US
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c:
Between 1995 and 1999 the US added an average of 13.05 million mobile subscribers per year.
The model indicates that in 1990 there were -31.45 million mobile subscribers in the US, but that's impossible, which tells us that the model is unreliable for years prior to 1995.
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d:
f(2012-1990) = 13.05*(2012-1990) - 31.45
f(2012-1990) = 255.65
the model predicts that in 2012 there will be 255.65 million of mobile subscribers in the US
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e:
That's probably not a good estimate. As we saw in part (c) above, the model is unreliable for years prior to 1995. Similarly, the model is likely to be unreliable for years after 1999. For example, the rate at which subscribers are added per year after 1999 could very well be higher or lower than the rate predicted by the model, and in fact the rate is likely to change from year to year non-linearly.
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