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belka [17]
3 years ago
6

In 1985, there were 285 cell phone subscribers in Arlington. The number of subscribers increased by 75% per year since 1985. Fin

d the number of subscribers in 2008.
Mathematics
1 answer:
ANTONII [103]3 years ago
8 0

Answer:

The number of subscribers in 2008 is 110,845,988

Step-by-step explanation:

The number of cell phone subscribers in Arlington, in t years after 1985, can be modeled by the following equation.

N(t) = N(0)(1+r)^{t}

And which N(0) is the number of subscribers in 1985 and r is the rate it increases per year, as a decimal.

In 1985, there were 285 cell phone subscribers in Arlington.

This means that N(0) = 285

The number of subscribers increased by 75% per year since 1985.

This means that r = 0.75

So

N(t) = 285(1.75)^{t}

Find the number of subscribers in 2008.

2008 is 2008-1985 = 23 years after 1985. So we have to find N(23).

N(23) = 285(1.75)^{23} = 110,845,988

The number of subscribers in 2008 is 110,845,988

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Answer:

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Previous concepts

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Solution to the problem

Part a

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And the standard error for the mean would be:

\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14

Part b

We want this probability:

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z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143

And we can find this probability with the complement rule and the normal standard deviation or excel and we got:

P( z>2.143) = 1-P(Z

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