Before surgery a patient might be injected with some medication.

When the concentration of the drug in the bloodstream is within a desired level the surgeon can operate.

You can model the concentration of the drug in the patient’s bloodstream using a rational function.

Here is a hypothetical rational function representing the concentration of a drug in the patient’s bloodstream with respect to time.

2

4)(

2 t

ttC

C(t)

t

If the drug concentration needs to be above 0.8 for the operation to take place, then we can use a rational inequality and determine the interval of time when the operation can take place.

8.02

42

tt

The inequality we would end up solving would be given by the following.

You can use rational functions to model what are known as average cost functions.

Average cost functions can help a business determine the cost of producing a certain product.

Suppose your company makes handbags and you want to determine the average cost of making hangbags.

You can model the average cost function for making handbags using the rational function shown below.

fixed cost to run business

cost of each handbag

number of handbags produced

Using this equation, if you wanted to determine when the average cost function is below a certain value, you would end up with a rational inequality.

Here, is an example of a rational inequality being used to determine when the average cost function is below 10000 dollars.

Solving this rational inequality can help to tell a business owner how many handbags he/she can make while staying under a certain budget.