Mathematical Models 10

10.1 Introduction

EMBAS

Up until now, you haveonly learnt how to solveequations and inequalities, but there has not been

much application of what you have learnt. Thischapter builds on this knowledge and introduces you

to the idea of a mathematical model, which uses mathematical concepts to solve real-world problems.

See introductory video:VMfjh at http://www.everythingmaths.co.za

10.2 Mathematical Models EMBAT

DEFINITION: Mathematical Model

A mathematical modelis a method of using the mathematical language to describe

the behaviour of a physical system. Mathematical models are used particularly in the

natural sciences and engineering disciplines (such as physics, biology, and electrical

engineering) but also inthe social sciences (suchas economics, sociologyand political

science); physicists, engineers, computer scientists, and economists usemathematical

models most extensively.

A mathematical modelis an equation (or a setof equations for the more difficult problems) that de-

scribes a particular situation. For example, if Anna receives R 3 for each time she helps her mother

wash the dishes and R 5 for each time she helpsher father cut the grass,how much money will Anna

earn if she helps her mother to wash the dishesfive times and helps herfather to wash the car twice?

The first step to modelling is to write the equation, that describes the situation. To calculate how much

Anna will earn we see that she will earn :

5 × R 3 for washing the dishes

+ 2× R 5 for cutting the grass

= R15 + R 10

= R 25

If however, we ask: ”What is the equation if Anna helps her mother x times and her father y times?”,

then we have:

Total earned = (x× R3) + (y× R5)