linearly word problems

Question

the revenue of kodak decreased approximately linearly from $19.0 billion on 1990 to $6.0 billion in 2100. The company is trying to emerge from bankruptcy protection in 2013. predict the revenue in that year

Answer 1

Hi Jennifer,

 

Since we know that this is an (approximately) linear relationship, we should identify our "x" and "y" parameters. In this case, I think it would be easiest to say that "x" refers to the year, and "y" refers to revenue. We can then turn the information into data points on a graph:

 

    When the year "x" was 1990, the revenue "y" was $19.0 billion

 

    When the year "x" was 2100, the revenue "y" was $6.0 billion

 

In other words, two (x,y) points on the graph are (1990,19) and (2100,6)    (disregarding the "billion" on the y value - we'll just have to remember to put that back on any "y" answer we come up with)

 

The equation of a line (the relationship between "x" and "y") can be expressed a few different ways, usually either the slope-intercept form (y=mx+b), where we have to know the slope and the y-intercept, or the point-slope form ((y-y₁)=m(x-x₁)), where we have to know the slope and any point on the line. Unless we happen to know the y-intercept, I prefer to use the point-slope format. In either case, we need to know the slope of the line

 

    Slope = Δy/Δx = rise/run = (6 - 19)/(2100 - 1990) = -13/110

 

We can now pick either of the points that we know to complete the (x₁,y₁) for the point-slope form of the equation of the line - I'll use (2100,6):

 

    (y-6) = -13/110*(x-2100)

 

Now, we can use algebra to transform this into the slope-intercept form:

 

    (y-6) = -13/110*(x-2100)

 

    y-6 = (-13/110)*x + 27300/110

 

    y = (-13/110)*x + 27300/110 + 660/110

 

    y = (-13/110)*x + 27960/110

 

Since we want to know the revenue "y" when the year "x" is 2013, we plug in 2013 for x:

 

    y = (-13/110)*(2013) + 27960/110

 

    y = 16.3 (rounded to three digits)

 

So for a linear relationship, in 2013, the revenue would be $16.3 billion

 

I hope this helps!

 

Andy