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

(a) 3178

(b) 14231

(c) 33152

Explanation:

Given

`y = (269573)/(1+985e^(-0.308t))`

Solving (a): Year = 1998

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

So:

`y = (269573)/(1+985e^(-0.308*8))`

`y = (269573)/(1+985e^(-2.464))`

`y = (269573)/(1+985*0.08509)`

`y = (269573)/(84.81365)`

`y = 3178` --- approximated

Solving (b): Year = 2003

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

So:

`y = (269573)/(1+985e^(-0.308*13))`

`y = (269573)/(1+985e^(-4.004))`

`y = (269573)/(1+985*0.01824)`

`y = (269573)/(18.9664)`

`y = 14213` --- approximated

Solving (c): Year = 2006

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

So:

`y = (269573)/(1+985e^(-0.308*16))`

`y = (269573)/(1+985e^(-4.928))`

`y = (269573)/(1+985*0.00724)`

`y = (269573)/(8.1314)`

`y = 33152` --- approximated