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

Volume, Rajun uses 2/3 of a carton of milk to make a pancake. The volume of...

Rajun uses 2/3 of a carton of milk to make a pancake. The volume of milk he uses is 800ml. calculate the volume, in l, of a milk in carton?

How will the decimal point move when 245.398 is multiplied, How will the de...

How will the decimal point move when 245.398 is multiplied by 100? It is moved two places to the right. While multiplying by multiples of 10, the decimal point is moved to the

Tangents with polar coordinates - parametric equations, Tangents with Polar...

Tangents with Polar Coordinates Here we now require to discuss some calculus topics in terms of polar coordinates. We will begin with finding tangent lines to polar curves.

Principle of superposition, If y 1 (t) and y 2 (t) are two solutions to a...

If y 1 (t) and y 2 (t) are two solutions to a linear, homogeneous differential equation thus it is y (t ) = c 1 y 1 (t ) + c 2 y 2 (t )   ........................(3) Remem

Find the maxima and minima - equal pi, 1) Find the maxima and minima of f(x...

1) Find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2) Compute the work done by the force ?eld F(x,y,z) = x^2I + y j +y k in moving

Factor expressions involving large powers, Factor Expressions Involving Lar...

Factor Expressions Involving Large Powers, Radicals, and Trig Functions You can use substitution to factor expressions involving large powers, radicals, and trig functions

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