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 2014 can be modeled by

y = 340,110/
1 + 377e−0.259t
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) 74553

(b) 172120

(c) 234802

Explanation:

Given

`y = (340110)/(1 + 377e^(-0.259t))`

Solving (a): 1998

Year 1998 means that:

`t =1998 - 1980`

`t =18`

So, we have:

`y = (340110)/(1 + 377e^(-0.259*18))`

`y = (340110)/(1 + 377e^(-4.662))`

`y = (340110)/(1 + 3.562)`

`y = (340110)/(4.562)`

`y = 74553` --- approximated

Solving (b): 2003

Year 2003 means that:

`t = 2003 - 1980`

`t =23`

So, we have:

`y = (340110)/(1 + 377e^(-0.259*23))`

`y = (340110)/(1 + 377e^(-5.957))`

`y = (340110)/(1 + 0.976)`

`y = (340110)/(1.976)`

`y = 172120` --- approximated

Solving (c): 2006

Year 2006 means that:

`t = 2006 - 1980`

`t =26`

So, we have:

`y = (340110)/(1 + 377e^(-0.259*26))`

`y = (340110)/(1 + 377e^(-6.734))`

`y = (340110)/(1 + 0.4485)`

`y = (340110)/(1.4485)`

`y = 234802` --- approximated