Write a linear model that represents the company's sales as a function of the number of years since 2006. Use the model to predict the sales in 2021.

Question

In 2006, a company had sales of $10 million. In 2011, sales were $12.5 million

Answer 1

The slope is (12.5 - 10)/(2011-2006) = 2.5/5 = 0.5

 

The intercept at year zer0 is 10

 

The linear model is f(x) =   0.5*(x-2006) + 10

 

Note that f(2011) = 0.5* (2011 - 2006) + 10 = 0.5 * 5 + 10 = 2.5 + 10 = 12.5 as expected.

 

f(2021) = 0.5*(2021 - 2006) + 10 = 0.5 * 15 + 10 = 7.5 + 10 = 17.5

 

$17.5 million = 17,500,000

 

 

Answer 2

We're going to call 2011 year 5 and 2006 year 0.

 

(12.5 - 10)/(5 - 0)= 2.5/5 = 0.5 million/year

 

y = 0.5x + 10 -----> The starting amount plus production per year, but in the algebraic order.

 

2021 would be year 15. Plug in 15 for x for your answer.