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REAL LIFE APPLICATION OF FUNCTIONS

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Sofia Mallari

on 19 August 2014

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Transcript of REAL LIFE APPLICATION OF FUNCTIONS

Real life application of rational functions
There are many ways of applying rational function in our lives. Examples of this are used in determining the ff:
Cost of living
Medical Dosage
Economic Production of Goods


C(t)= 4t
t^2+2
Did you say functions?
Rational Function
A rational function is a function that can be represented through an equation in this form :

f(x) = p(x)/ g(x)


***both p(x) and g(x) are polynomial functions, where g(x) cannot equal to 0.


REAL LIFE APPLICATION OF FUNCTIONS
What are the different types of function
that will be discussed?

Using Rational Functions
in Medical Dosage

1.) Rational Function
2.) Linear Function
3.)Exponential
Function


When medicine is given overtime
a certain amount is going to be
absorbed in the body so we
need to know the exact amount
of the medicine that is existing
in that body in a certain
period of time. We will use the
rational function in determining
the concentration of the medicine
in the body.

This is a hypothetical rational function representing the
concentration of a drug in the
patient’s bloodstream with
respect to time.
Rational function: real world problem
What will the concentration, in ppm, of the drug be after 4 hours?

Use the given formula: where C = concentration in ppm and t = number of hours


C(t)= 4t
t^2 + 2
= 4 (4)
(4)^2 + 2
= 16


18
or
= 8
9
From calculating, we know that after
4 hours of injecting the drug,
the concentration of the patient's
blood will be 8 ppm.
9
Visual representation
What is Linear Function?
A function f is linear if it can be expressed in the form :

f ( x) = mx + b

where m and b are constants and x is an arbitrary member of the domain of f. Often the
relationship between two variables x and y is a linear function expressed as an
equation y = mx + b .
Some Real - Life Applications of
Linear Functions
Cost of the purchased item
Total hours of travel and distance
Transport fare
and fuel pump price

Using Linear function on

Transport fare and fuel pump price

The approach adopted in this study is the use of mathematical model in the form of a linear equation to investigate the impact of subsidy removal on the standard of living of the people and its long term economic effect. This is used to analyze the correlation between fuel pump price and transportation.
Linear Application Explanation
from a Real Situation
The purpose of this section is to establish the relationship between the two variables (fuel pump price and transport fare), and their corresponding values gotten from the survey. Which is similar to the equation of a straight line y = mx + c, which is a first degree equation.

m= N -economical factor
c= intercept of fuel price and
transport fare.
Survey Given
Considering this we plot a graph of fuel price against transport fare. It is represented mathematically as
m= ( change in transport fare)
(change in fuel price current purchase value of naira)


CPVN = (change in transport fare)
(change in fuel price)

For example 2012 purchase value of one hundred naira is :
X (any naira denomination)
CpVN2012 = 40 x N100


m= 52.60
70
we can further deduce the value
of c from the following equation
Given that T = mF + c or Y=mx+b
such that if c = 0; change in
T = m(change in F)
from the table1, we could deduce that
(T-5) = 52.6(F-0.5)
F = 52.6T – 26.3 + 5 F = 52.6T – 21.3
This implies that c = -21.3
The negative sign gotten from the intercept shows that there was a point in time when fuel was practically gotten for free by Nigerians, that was actually before the first fuel hike in the country.
Therefore we can derive an equation for the economy of Nigeria which is
F= 52.6T – 21.3.
The value for the application of this equation is gotten from table1; it is a further explanation of the effect of fuel hike on the actual purchasing power of naira.



Some Real - Life Applications of Exponential Linear Functions
What is exponential functions?
Exponential functions look somewhat similar to
functions you have seen before, in that they involve exponents,
but there is a big difference, in that the variable is now the power,
rather than the base.

Previously, you have dealt with such
functions as f(x) = x^2, where the variable x
was the base and the number 2 was the power.
In the case of exponentials,
however, you will be dealing with functions such as g(x) = 2^x,
where the base is the fixed number, and the power is the variable.

Population Growth
Interest
Exponential decay
Exponential Function: Real Life application
Population Growth
Exponential functions are quite used to
model population growth

Consider this example:
Suppose there is a social networking website.
Every week, every member of the site recruits one
more person to join the site.
If there are 10 members initially, graph the number of
members of the site versus time.




If every member recruits a new
member each week, the population of the site
doubles. Thus, each week, the population of the site
is multiplied by two. If there are ten initial members,
our model will be y = 10 * 2t.

Let's zoom in!
The population
of the site is over
1000 people in
just over 6
weeks!
Populations that
grow
exponentially are
very fast-
growing.
By: Sofia Mallari
and Ivan Ichon
Full transcript