Chapter 3.5, Problem 41E

Cell Sites A cell site is a site where electronic communication equipment is placed in a cellular network for the use of mobile phones. The number $y$ of cell sites from $1985$ through $2014$ can be modelled by

$y=\frac{320,110}{1+374e^{-0.252t}}$

Where t represents the year, with $t = 5$ corresponding the $1985$.

$\left(\mathrm{a}\right)$ Use the model to find the number of cell sites in the years $1998,\mathrm{ }2003\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }2006$,

$\left(\mathrm{b}\right)$ Use a graphing utility to graph the function.

$\left(\mathrm{c}\right)$ Use the graph to determine the year in which the number of cell sites reached $\mathrm{270,000}$.

$\left(\mathrm{d}\right)$ Confirm your answer to part $\left(\mathrm{c}\right)$ algebraically.