Chapter 2 Linear Equations and Functions - 2.2 Find Slope and Rate of Change - Guided Practice for Example 5 - Page 85: 13

$258.5$ inches.

By using the slope formula, the average rate of change is: $m=\frac{251-248}{2005-1965}=\frac{3}{40}=0.075.$ inch per year. There are $100$ years until 2105, thus by that time the increase will be $100\cdot0.075=7.5$. Thus the diameter will be $251+7.5=258.5$ inches.