10 Surprising Real-life Examples Of Rational Functions

It is interesting to find various examples of mathematics around us. Even more interesting is how these concepts influence us daily without our knowledge. If we carefully look around, we will find math influencing us more than any other subject from our school years. That’s the power of mathematics. 

Although, there is no hiding that math is one of the trickiest subjects. It required advanced critical thinking and a flexible mindset to adapt and apply the mathematical concepts around us. But there is no going back once we can identify and apply math around us. 

This article will take you through some real-life examples of rational functions. Go through them and see if you already know how rational function impacts the mentioned areas. 

But for those new to this concept, let’s first understand rational functions. 

What are rational functions?

If you think Rational function sounds like a tricky and lengthy concept that will be challenging to grasp, you should reconsider. Rational function, in reality, is one of the simplest concepts that can make challenging and advanced-level problems easy to solve. 

A rational function is nothing but a ratio of two polynomial values. The term rational implies that one numerator and one denominator can be divided by each other, just like a ratio.  

Now, what are polynomial values? It is an expression that involves constant values, exponents, or variables. These are combined using arithmetic operations, that is, addition, subtraction, multiplication, and division. 

Considering the above statements, we can represent a rational function as- 

3x² + 2y – 5
7a² × 4 ÷ 2b

Remember, the denominator can be any value but zero. 

Let’s try understanding rational functions using an example. 

Suppose you are on a road trip with your friends. You want to find the total time you took to reach your destination, including all the distractions and delays. There was bad traffic where you were stuck for many hours, represented by 5t and the finished fuel, represented by 3t². Let’s say 10t is your total distance. 

Using the given equation, we can form a rational function equation as,

Time (t) = 10t / 5t + 3t²  

Rational function in real life: A few examples 

There are many ways to get a hang of mathematical concepts, such as math manipulatives, online games, activities, etc. Real-life examples are one such way that is fun yet brain stimulating. Let’s see some real-life examples of rational functions. 

1. Is your speed, distance, and Time calculations…. accurate? 

Identifying the examples of rate of change around us is a great way to find rational functions in real-life. Rational function  helps to identify the speed, distance, and time of the objects in motion. For instance, when you try to calculate how long it will take you to reach your destination in extreme traffic hours, it is the rational function you are using. 

2. Trust your doctor! 

 Trust your doctor! 

Any medical treatment or procedure that involves constant monitoring of the rate of change of any drug in the body or body vitals, such as blood pressure, glucose level, etc., represents rational functions in real-life. For instance, when a doctor injects you with a drug at an interval of a specific time, the doctor constantly tracks your body vitals before and after every dose to maintain a constant and healthy condition. To keep a record, doctors use rational functions. 

Similarly, keeping track of the time when some hazardous medical waste will decay, considering different environmental conditions, is an example of a rational function. 

3. How sloppy are your Supply and demand curves? 

How sloppy are your Supply and demand curves? 

Another real-life example of a rational function is the supply and demand curves and other economically relevant processes. There is a constant cycle of supply of products and their demand in the market. With such high demand, keeping track of all taxes and market dynamics is highly important to prevent any potential economic loss.

Also, fixing a suitable price that is flexible to a particular demographic, but justifying other additional expenses is important. All these processes are an example of rational functions in real-life. 

4. Are your costs and revenue bringing you profit? 

Are your costs and revenue bringing you profit? 

If you are a businessman, you know how rational functions save the day when calculating the cost of the products and the revenue generated from them. Or you might be a frustrated student trying to calculate the cost and selling prices of products for your math homework.

All you have to do is identify all the factors involved with the overall cost and revenue, and you have your profit, loss, CP, and SP calculated in minutes or maybe hours. And it’s that easy with rational functions. 

5. Careful! The Electrical circuits are functional! 

Careful! The Electrical circuits are functional! 

Have you ever wondered how current flows in electrical circuits? Or why the voltage impacts the flow of current in the circuits? Or how do physicists assess the rate of flow of current? These are the classic examples of rational functions in real-life. Several factors impact the current flow and electrical circuits’ functioning, which can be calculated using rational functions. 

6. Population growth is constantly un-constant! 

. Population growth is constantly un-constant

Our natural resources are rapidly depleting, and the population is constantly increasing. By this observation, how long can we expect the justified distribution of resources among all people? How are external factors impacting the rate of depletion of resources?

Questions like these are answered using a logistic growth model, a great example of rational functions in real-life. It helps to understand and predict how fast, moderate, or slow the resources will deplete. 

7. Is your Investment functionally secure?  

Is your Investment functionally secure? 

Have you ever noticed numerous conditions when investing in stocks or fixing a certain amount of money? Based on those conditions, you receive your final amount with earned profit. This is an example of a rational function in real-life.

Investors assess the factors impacting their money and use rational functions to identify and predict the final value. Similarly, the calculation of interests on assets and risk assessment is carried out using rational functions. 

8. Is your Chemical concentration relevant? 

Is your Chemical concentration relevant? 

In real life, performing experiments with chemicals and developing chemical equations are great examples of rational functions. Rational functions help determine how much concentration of a chemical will vary and at what time, keeping external conditions constant or changing. Various factors must be regulated while performing any chemical experiment, and rational functions are a great way to identify and regulate them.

9. How does your guitar produce music? 

How does your guitar produce music? 

Have you ever wondered how guitars and other musical instruments produce music? Beating the drum can be a noise, but how do musicians make it a melody? It is because of the vibrations that are produced by those musical instruments. And assessing how the change in the vibrations produces different musical melodies is an example of a rational function in real-life. 

10. The temperature control system requires input and output signals. 

The temperature control system requires input and output signals

The temperature control system requires the input and output signals to function properly. Input signal might involve the setpoint temperature and output signal might involve the change in temperature done manually. These signals are an example of rational functions used to assess and analyze different temperature-related aspects such as temperature regulation, automation, and motor control. 

Concluding thoughts 

For many children, achieving an advanced understanding of rational functions is a mathematical goal. After all, the concept is widely used in numerous domains, making it a must to understand. The above-mentioned real-life examples help us understand how the concept is utilized in our day-to-day activities. Rational functions are an example of adaptive learning and can easily be understood and applied with the right strategies and consistent efforts. 

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