Question

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

Answer 1

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