Fitting Exponential Models to Data · Try It 3

The table shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012.

$$\begin{array}{cccc}\text{Year}& \text{Seal Population (Thousands)}& \text{Year}& \text{Seal Population (Thousands)}\\ \text{1997}& \text{3.493}& \text{2005}& \text{19.590}\\ \text{1998}& \text{5.282}& \text{2006}& \text{21.955}\\ \text{1999}& \text{6.357}& \text{2007}& \text{22.862}\\ \text{2000}& \text{9.201}& \text{2008}& \text{23.869}\\ \text{2001}& \text{11.224}& \text{2009}& \text{24.243}\\ \text{2002}& \text{12.964}& \text{2010}& \text{24.344}\\ \text{2003}& \text{16.226}& \text{2011}& \text{24.919}\\ \text{2004}& \text{18.137}& \text{2012}& \text{25.108}\end{array}$$

ⓐ Let $x$ represent time in years starting with $x=0$ for the year 1997. Let $y$ represent the number of seals in thousands. Use logistic regression to fit a model to these data.
ⓑ Use the model to predict the seal population for the year 2020.
ⓒ To the nearest whole number, what is the limiting value of this model?

OpenStax, Algebra and Trigonometry 2e · §6.8 Fitting Exponential Models to Data · Try It 3