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

Unit rates, which shows the rate 12 inches of rain in 6 hours as a unit rat...

which shows the rate 12 inches of rain in 6 hours as a unit rate

3/8:5/9, how do I change this ratio to a fraction

how do I change this ratio to a fraction

, What is 124 out of 300 in percent

What is 124 out of 300 in percent ?

Math, what is the changen intemperature bewtween the highest and the lowest...

what is the changen intemperature bewtween the highest and the lowest temperture high-40c low-0c

Find no. of diagonals, In a polygon no 3 diagnols are concurrent. If the to...

In a polygon no 3 diagnols are concurrent. If the total no of points of intersection are 70 ( interior ). find the no. of diagnols? Ans) Since no 3 diagonals are concurrent, There

Example of developing an understanding, In class 1, the teacher had written...

In class 1, the teacher had written down the digits 0,1, ...., 9 on the board. Then she made all the children recite the corresponding number names. Finally, she made them write th

Mode, how to work out mode

how to work out mode

Important formulas of functions , Important formulas d (a b )/ dx  = 0...

Important formulas d (a b )/ dx  = 0                              This is a constant d ( x n ) / dx = nx n -1                      Power Rule d (a x ) / dx = a x l

Pair of st line, #qu Given the equation through what angle should the axes...

#qu Given the equation through what angle should the axes be rotated so that the term in xy be waiting from the transformed equation. estion..

Can religious wars be avoided in the future, To what extent do you think re...

To what extent do you think religious beliefs should justify war? How is this shown in "The Song of Roland"? Cite examples of how religious beliefs have led to war in the last two

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