Chapter 2.5, Problem 28E

Diabetes As the following table shows, projections indicate that the percent of U.S. adults with diabetes could dramatically increase.

$\begin{array}{llllll}\text{Year}\hfill & \text{Percent}\hfill & \text{Year}\hfill & \text{Percent}\hfill & \text{Year}\hfill & \text{Percent}\hfill \\ \text{2010}\hfill & \text{15}\text{.7}\hfill & \text{2025}\hfill & \text{24}\text{.2}\hfill & \text{2040}\hfill & \text{31}\text{.4}\hfill \\ \text{2015}\hfill & \text{18}\text{.9}\hfill & \text{2030}\hfill & \text{27}\text{.2}\hfill & \text{2045}\hfill & \text{32}\text{.1}\hfill \\ \text{2020}\hfill & \text{21}\text{.1}\hfill & \text{2035}\hfill & \text{29}\text{.0}\hfill & \text{2030}\hfill & \text{34}\text{.3}\hfill \end{array}$

Find a linear model that fits the data in the table, with $x$ as the percent of year in $2000$.

Use the model to predict the percent of U.S. adults with diabetes in $2018$.

In what year does this model predict the percent of U.S adults with diabetes will reach $25\%$?