Transcript Real World Rational Inequalities


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.
C(t)
4t
C (t )  2
t 2
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.
The inequality we would end
up solving would be given by
the following.
4t

0
.
8
2
t 2
 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
number of
handbags
produced
cost of each handbag
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.