# Modeling and Applications Learning

Mathematical modelling is an abstract model that uses mathematical language to describe the behavior of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively.

## Applications for modeling on modeling and applications learning

The following applications will helps for Learning applications of modeling.

• The modeling can be used for identification of fingerprints.

• The modeling can be used  in private health insurance.

• The modeling can be used  for methodical problems of fishing sciences.

• Using in optimal position of rescue helicopters in south Tyrol.

• In ratio therapy planning for cancer patients.

• It can be used  in pricing for internet booking of flights.

• The modeling applications are used  in some risk management.

## Examples on modeling and applications learning

The following figure helps for learning the modeling process and its applications

Example problems for learning the applications of modeling:

Suppose Ramesh has invested Rs.15000 at 8% simple interest per year. With the return from the investment, he wants to buy a washing machine that costs Rs.19000. for what period should he invest Rs.15000 so that he has enough money to buy a washing machine?

Solution:

Step 1:

The formula for simple interest is   Pnr

I =   --------

100

Where, P = principle

n = number of years

r % = rate of interest

I = interest earned

Here, the principle = Rs.15000

The money required by ramesh for buying a washing machine = Rs19000

So, the interest to be earned = Rs (19000 - 15000)

= Rs 4000

The number of years for which Rs 1500 is deposited = n

The interest on Rs 1500 for n years at the rate of 8% = I

Then,                               15000 *  n * 8
=  -------------------
100

So,               I = 1200n (1)

This gives the relationship between the number of years and interest, if Rs 15000 is invested at an annual rate of 8%.

We have to find the period in which the interest earned is Rs4000.

Putting I = 4000 in (1), we have

4000 = 1200n

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Step 2:

Solving Equation (2) we get

n = 4000/1200
= 3 1/3

Step 3:

Since n = 3  1/3 and one third of a year is 4 months,

Ramesh can buy a washing machine after 3 years and 4 months.