Question

According to the Association of American Railroads, Class I freight railroads are the line-haul freight railroads with 2006 operating revenue in excess of $346.8 million. Let F = F(t) denote the freight revenue in billions of dollars of Class I railroads in year t. In 2005, Class I railroads had a freight revenue of $44.5 billion. In 2007, the revenue was $52.9 billion. Calculate the average rate of change per year in F from 2005 to 2007.

Answer 1

The average rate of change per year in F from 2005 to 2007 is $4.2 billion/year.

Step-by-step explanation:

Let F = F(t),

It represents freight revenue in billions of dollars of Class I railroads in year t.

It is given that in 2005, Class I railroads had a freight revenue of $44.5 billion. In 2007, the revenue was $52.9 billion.

f(2005)=$44.5

f(2007)=$52.9

If a linear function passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the formula for rate of change is

`m=(f(x_2)-f(x_1))/(x_2-x_1)`

The average rate of change per year in F from 2005 to 2007 is

`m=(f(2007)-f(2005))/(2007-2005)`

`m=(52.9-44.5)/(2)`

`m=(8.4)/(2)`

`m=4.2`

Therefore the average rate of change per year in F from 2005 to 2007 is $4.2 billion/year.