The polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck is:
[tex]f(x) = -0.04x^2 + 18x + 75[/tex]
Solution:
The cost of distributing by train can be modeled as:
[tex]-0.07x^2 + 40x - 105[/tex]
The cost of distributing by truck can be modeled as:
[tex]-0.03x^2 + 22x - 180[/tex]
where x is the number of tons of product distributed
To find: Difference between the cost of distributing by train and the cost of distributing by truck
Difference = cost of distributing by train - cost of distributing by truck
Let f(x) = difference in cost between trains & trucks
[tex]f(x) = (-0.07x^2+40x-105) - (-0.03x^2 +22x - 180)[/tex]
[tex]f(x) = -0.07x^2 + 40x -105 + 0.03x^2 -22x + 180[/tex]
[tex]Combine\ the\ like\ terms\\\\f(x) = -0.07x^2 +0.03x^2 + 40x - 22x +180-105\\\\Add\ the\ like\ terms\\\\f(x) = -0.04x^2 + 18x + 75[/tex]
Thus polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck is found