Contents

# Model|Definition & Meaning

## Definition

A **mathematical model** is something that describes the **behavior** of a system using **mathematical language**. A mathematical model is made up of a **equation** or **group of equations** that describe the dynamic behavior of the corresponding system and belong to a specific class of mathematical models.

A **mathematical model** is a system description that employs mathematical **language** and **concepts**. Mathematical modeling is the process of creating a mathematical model. Mathematical models are employed in the natural sciences, engineering, and non-physical processes, such as in the social sciences.

## The Need for Mathematical Modeling

A Mathematics Model seems to be when we use math concepts and ideas to ‘**model**‘ a **real-world object** or **situation**. This can help us understand the real world and can be employed to improve many aspects of our lives. These models are vital to the working world, from safety to planning and construction.

More broadly, a model is a representation of an **idea **or **object** that is used to gain a better understanding of the real thing. A Model of a house, for instance, is used to demonstrate the design and layout of a real house before it is purchased or constructed.

Estimated measurements are used in mathematical models to help us be more **precise** when planning what we can do with the **real version** of **objects**.

## Checking the Precision of a Mathematical Model

Mathematical Models are representations of **real-life objects,** but they are not inherently perfectly accurate depictions of reality. We did not even consider other real-world factors in our examples, such as the cardboard’s size, the weight the box could hold, or if it would split apart when we used it to transport liquids. Most of these objects could be anticipated using more complex mathematical models, but remember that the model is only an **estimate**.

Some scientists use extremely accurate, complex models for critical tasks such as space exploration, which necessitates accurate estimation with little room for error.

However, for our applications, a simple model will be easier. The important question arrives here is determining whether that model is **appropriate** for the task at hand or not. If we are required to understand how many key components we might accommodate in the box, knowing the volume in the meter cube within that box would be incredibly helpful.

## Classification of Models

On an implementation basis, we can categorize mathematical models into two main categories, which are further divided into two subcategories.

- Analytical
- Algorithmic

The two main **categories,** which are analytical and algorithmic, are further divided into **two** subcategories. Analytical has **Algebraic** and **Approximation** methods, whereas **Algorithmic** categories have **Numeric **and **Simulation **subdivisions.

## Types of Mathematical Models

Mathematical models can be found all over the school levels. One of the most common types that we see in everyday life are **equations**, **statistics**, and **graphs**. The mathematical model for calculating any shape’s volume, area, or parameter is an equation.

The most commonly used mathematical model is an **equation**. Scientists like **Albert Einstein** used equations to build a sense of their surroundings. However, even young children in primary school will learn to use very basic equations, which will help them understand the **concepts** and **factors** behind their use.

Many mathematical models can be utilized to forecast what will occur in any given situation. Mathematical models, for example, are used to **forecast** the weather. This could tell you whether or not you should carry a coat to school.

However, it may also notify a business owner, such as an ice cream vendor, how many customers to expect in the park. It might even assist us in preparing for major storms.

### Pie Chart

Mathematical models include **pie charts**,** line graphs**, and **bar charts**. They’re even used to discuss key points regarding large groups of statistics and numbers.

The mathematical model above is a pie chart showing how many students like different subjects. Here, **35 **students like Computer, **20** students like Maths, **15** Students like Science, and **30 **students like English.

### Line Graph

Here is another mathematical model of a **line graph **which shows the temperature of a city that changes with time during a whole day.

The above model describes the **temperature **of a city that how temperature falls and rises with **time**. From this model, it becomes very easy for people to see the rise and fall of the temperature. So the mathematical model is very important in temperature prediction as well.

### Equation

We just used a mathematical model that consisted **equation** or **formula**. But the common type of mathematical model is an **equation**.

## Examples of Mathematical Modeling

### Example 1

Jack plans to invest in some businesses that will return a profit of 20% per year. What will be the total money he gets at the end of the year?

### Solution

Jack’s initial amount = x

Profit Jack gets per year = 20%

Total money Jack gets at the end of year = ?

Total money = x + (20%)x

20% = 20 ⁄100 = 0.2

Put the value of 20% in the above equation

**Total money = x + 0.2x**

### Example 2

### Solution

Length of field = 285 m

Cost to level the field = 20 cents per square meter

Area of square = side²

here length = side

Area of square = 285²

Area of square = 285 x 285

Area of square = 81225 m²

Cost to level the area = 20 x 81225

**Cost to level the area = 1624500 cents**

*All the above figures are created in GeoGebra.*