Word problem college algebra

Question

Assume that the annual sales of a small manufacturer can be modeled by a linear function and that sales where $25,500 in 2008 and 57,500 in 2013. Let x=0 represent 2008 and f(x) represent annual sales, and write a formula for f(x).

Answer 1

 

Since this is a linear model, 2 points on the line using given data are:

 

    (0, 25500)  and (5, 57500)  ... 0 is year 2008, 5 is year 2013 (5 years after 2008)

 

We can use the slope formula to find the slope of the line.

 

    (x₁, y₁) = (0, 25500) 

    (x₂, y₂) = (5, 57500)

 

    m = (y₂ - y₁) / (x₂ - x₁)

 

    m = (57500 - 25500)/(5 - 0)

    m = 32000/5

    m = 6400

 

The y-intercept of the equation is 25550 because the x-coordinate at that y-value is 0

 

Using the point slope formula,

 

   y = mx + b

   

   y = 6400x + 25500   ... where x = number of years after 2008

 

So the function is

 

   f(x) = 6400x + 25500