1. Rational Functions in the Real World
Powered by: Mr. Michael Angelo B. del Rosario
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2. Objectives
At the end of the lesson, the learner is expected to:
demonstrates understanding of key concepts of rational functions.
accurately solve real life problems involving rational functions.

3. What have we learned? What is a rational number?
So just for grins, what is an irrational number?
A rational function has the form
A number that can be expressed as a fraction:
A number that cannot be expressed as a fraction:

4. Medical Example
After learning all the stuffs in rational functions, when and how are we going to use this skill?
How can we apply the graphs of rational function in real life situation?

5. Medical Example

6. Medical Example
Before surgery a patient might be injected with some medication.
When the concentration of the drug in the bloodstream is at a desired level the operation will begin.
You can model the concentration of the drug in the patient’s bloodstream using a rational function.

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

8. Medical Example Graph
C(t) t

9. Medical Example Cont’d
Being able to analyze this rational function can help a nurse or doctor determine when the drug will wear off on the patient.
Imagine not knowing how to do this and having a patient wake up during surgery.

10. Medical Example Graph
Let us analyze the graph by answering the following question.
C(t)
What is the highest level of concentration C(t) of drug in the patients bloodstream?
Aside from time(t) zero, will the concentration C(t) of the drug become zero again? t

11. Economic Example

12. Economic Example
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.

13. Economic Example Cont’d
Suppose your company makes light bulbs and you want to determine the average cost of making light bulbs.

14. Economic Example Cont’d
You can model the average cost function for making light bulbs using the rational function shown below.
fixed cost to run business
cost of each light bulb
number of light bulbs produced

15. Economic Example Cont’d
Using this rational function, you can model how much it will cost to make light bulbs, which can be important information for a businessman.

16. Sample Problems
The weekly sale (S) (in thousands of units) for the tth week after the introduction of the product in the market is given by 𝑆= 120𝑡 𝑡 In which week would the sale (S) have been 6?

17. Sample Problems
After taking a certain antibiotic, the concentration (C) of the drug in the patient's bloodstream is given by 𝐶 𝑡 = 0.04𝑡 𝑡 2 −2 , where t is the time (in hours) after taking the antibiotic. How many hours after taking the antibiotic will its concentration be 0.04 units?

18. Sample Problems
The average cost per unit C(x), in dollars, to produce x units of toy cars is given by 𝑆= 8000 𝑥−50 . What is the approximate cost per unit when 1250 toy cars are produced?

19. References
Comandante, Felipe Jr. L., Algebra Made Easy,