In 2006 a company had sales of 10 million. In 2011 sales were 12.5 million. Write a linear model that represents the company's sales as a function of the number of the years since 2006. Use the model?

To create a linear model representing the company's sales as a function of the number of years since 2006, we can define ( t ) as the number of years since 2006. The sales in 2006 (when ( t = 0 )) were 10 million, and in 2011 (when ( t = 5 )), sales were 12.5 million. The slope of the line can be calculated as ( \frac{12.5 - 10}{5 - 0} = 0.5 ) million per year. Thus, the linear model is ( S(t) = 10 + 0.5t ).

Using this model, if we want to find the sales in 2013 (when ( t = 7 )), we can substitute ( t ) into the equation: ( S(7) = 10 + 0.5 \times 7 = 10 + 3.5 = 13.5 ) million.