Exponential functions, Mathematics

Assignment Help:

The exponential functions are useful for describing compound interest and growth. The exponential function is defined as:

         y = m. ax

where 'm' and 'a' are constants with 'x' being an independent variable and 'a' being the base.

The exponential curve rises to the right for a > 1 and m > 0 and rises to left for a < 1 and m > 0.

If x takes on only positive integral values (1,2, 3,...), y = max is the x-th term in a Geometric Progression.

Figure 

1744_exponential function.png

Example 

Compound interest can be shown to be an exponential function. If we invest A rupees in a bank that pays r% compound annual interest then,

y1      =       A + Ar = A (1 + r)

         =       amount your money will grow at the end of the first year.

y2      =       A(1 + r) + A(1 + r)r

         =       A(1 + r) (1 + r)

         =       A(1 + r)2

         =       amount your money will grow at the end of second year.

In general,

yn      = A(1 + r)n       

This expression is of the form y = m.ax where the value of 'm' is A and the value 'a' is (1 + r). The money grows exponentially when it is paid compound interest.


Related Discussions:- Exponential functions

Divides a given line segment internally in the ratio of 1:3, Divides a give...

Divides a given line segment internally in the ratio of 1:3 Construction : i )Draw a ray AX making an acute angle with AB. ii) Mark 4 points at equal distance. on AX Let

Simplify, X^2 – y^2 – 2y - 1

X^2 – y^2 – 2y - 1

What is the maximum volume of rectangular box, 1. A rectangular piece of ca...

1. A rectangular piece of cardboard measuring 26 inches by 42 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side

#title applications of vector and scalar , #question application of vector ...

#question application of vector and scalar in our daily life

LINEAR EQUATIONS, SOLVE THE inequation 0>-5 -X AND X Belongs TO R .Represen...

SOLVE THE inequation 0>-5 -X AND X Belongs TO R .Represent THE SOLUTION SET ON THE NUMBER LINE

Find out the linear approximation, Find out the linear approximation for a...

Find out the linear approximation for at x =8 .  Utilizes the linear approximation to approximate the value of  and Solution Since it is just the tangent line there

Solve the differential equation, Solve the subsequent differential equation...

Solve the subsequent differential equation and find out the interval of validity for the solution. Let's start things off along with a fairly simple illustration so we can notic

Describe the properties of inequalities, Describe the Properties of Inequal...

Describe the Properties of Inequalities ? Postulate In comparing two quantities, say a and b, there are exactly three possibilities. (1) a is less than b. (a b)

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd