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nata0808 [166]
3 years ago
9

A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. Th

e numbers y of cell sites from 1985 through 2011 can be modeled byy = 269573/1+985e^-0.308t where t represents the year, with t = 5 corresponding to 1985. Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006.
Mathematics
1 answer:
netineya [11]3 years ago
5 0

Answer:

(a) 3178

(b) 14231

(c) 33152

Step-by-step explanation:

Given

y = \frac{269573}{1+985e^{-0.308t}}

Solving (a): Year = 1998

1998 means t = 8 i.e. 1998 - 1990

So:

y = \frac{269573}{1+985e^{-0.308*8}}

y = \frac{269573}{1+985e^{-2.464}}

y = \frac{269573}{1+985*0.08509}

y = \frac{269573}{84.81365}

y = 3178 --- approximated

Solving (b): Year = 2003

2003 means t = 13 i.e. 2003 - 1990

So:

y = \frac{269573}{1+985e^{-0.308*13}}

y = \frac{269573}{1+985e^{-4.004}}

y = \frac{269573}{1+985*0.01824}

y = \frac{269573}{18.9664}

y = 14213 --- approximated

Solving (c): Year = 2006

2006 means t = 16 i.e. 2006 - 1990

So:

y = \frac{269573}{1+985e^{-0.308*16}}

y = \frac{269573}{1+985e^{-4.928}}

y = \frac{269573}{1+985*0.00724}

y = \frac{269573}{8.1314}

y = 33152 --- approximated

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