Using Logistic Regression to Fit a Model to Data

Mobile telephone service has increased rapidly in America since the mid 1990s. Today, almost all residents have cellular service. The table shows the percentage of Americans with cellular service between the years 1995 and 2012.

\begin{array}{|c|c|c|c|}\hline \text{Year} & \text{Americans with Cellular Service (%)} & \text{Year} & \text{Americans with Cellular Service (%)} \\ \hline \text{1995} & \text{12.69} & \text{2004} & \text{62.852} \\ \hline \text{1996} & \text{16.35} & \text{2005} & \text{68.63} \\ \hline \text{1997} & \text{20.29} & \text{2006} & \text{76.64} \\ \hline \text{1998} & \text{25.08} & \text{2007} & \text{82.47} \\ \hline \text{1999} & \text{30.81} & \text{2008} & \text{85.68} \\ \hline \text{2000} & \text{38.75} & \text{2009} & \text{89.14} \\ \hline \text{2001} & \text{45.00} & \text{2010} & \text{91.86} \\ \hline \text{2002} & \text{49.16} & \text{2011} & \text{95.28} \\ \hline \text{2003} & \text{55.15} & \text{2012} & \text{98.17} \\ \hline\end{array}

ⓐ Let $x$ represent time in years starting with $x=0$ for the year 1995. Let $y$ represent the corresponding percentage of residents with cellular service. Use logistic regression to fit a model to these data.
ⓑ Use the model to calculate the percentage of Americans with cell service in the year 2013. Round to the nearest tenth of a percent.
ⓒ Discuss the value returned for the upper limit, $c.$ What does this tell you about the model? What would the limiting value be if the model were exact?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §6.8 Fitting Exponential Models to Data · Example 5