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

Answer:

(a) 74553

(b) 172120

(c) 234802

Step-by-step explanation:

Given

$y = \frac{340110}{1 + 377e^{-0.259t}}$

Solving (a): 1998

Year 1998 means that:

$t =1998 - 1980$

$t =18$

So, we have:

$y = \frac{340110}{1 + 377e^{-0.259*18}}$

$y = \frac{340110}{1 + 377e^{-4.662}}$

$y = \frac{340110}{1 + 3.562}$

$y = \frac{340110}{4.562}$

$y = 74553$ --- approximated

Solving (b): 2003

Year 2003 means that:

$t = 2003 - 1980$

$t =23$

So, we have:

$y = \frac{340110}{1 + 377e^{-0.259*23}}$

$y = \frac{340110}{1 + 377e^{-5.957}}$

$y = \frac{340110}{1 + 0.976}$

$y = \frac{340110}{1.976}$

$y = 172120$ --- approximated

Solving (c): 2006

Year 2006 means that:

$t = 2006 - 1980$

$t =26$

So, we have:

$y = \frac{340110}{1 + 377e^{-0.259*26}}$

$y = \frac{340110}{1 + 377e^{-6.734}}$

$y = \frac{340110}{1 + 0.4485}$

$y = \frac{340110}{1.4485}$

$y = 234802$ --- approximated