Real World Applications – Algebra I
How can we lower workers’ compensation in companies using Algebra?
We can represent this revised model by taking the difference between the two relationships as one rational expression.
In the picture above, we found the common denominator by making the denominators the same, and then we simplified the numerator.
What does this resulting expression mean?
We can input some values into a table for this function and make graph the relationship. It would look like this:
The graphs are really close together, so it’s a little difficult to compare. So, let’s take a look at the tables that represent the two relationships.
# of hours of training
||Without plan||With plan|
Looking at this table, we can see that the plan will definitely make a difference. For every number of hours of training, we can see that the rightmost column has significantly lower numbers. The plan will work!
After using the quadratic formula, we’ve found two answers. Would both answers make sense in this situation? And what do these answers mean?
Since we’re trying to find out how many trainings it would take to ensure that the number of incidents are no more than 5, 9.5 would make sense. Offering -10.5 trainings wouldn’t make sense!
Research different companies that would represent a similar type of model. Why would this company have this type of model? Why did you choose this company? Would this model be limited to injuries? What about production of certain goods?