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

Elliptic paraboloid - three dimensional spaces, Elliptic Paraboloid Th...

Elliptic Paraboloid The equation which is given here is the equation of an elliptic paraboloid. x 2 /a 2 + y 2 /b 2 = z/c Like with cylinders this has a cross section

Analysis, Ask question #Minimum 1Let X be a topological space, let p ? X, a...

Ask question #Minimum 1Let X be a topological space, let p ? X, and let F and ? be C-valued functions on X that are continuous at p. Then the functions F + ?, F?, |F|, ReF and ImF

Incircle, ab=8cm,bc=6cm,ca=5cm draw an incircle.

ab=8cm,bc=6cm,ca=5cm draw an incircle.

Hello, I am here to tell you, Alex has a cold.

I am here to tell you, Alex has a cold.

What is a lattice, What is a lattice? Which of the following graphs are lat...

What is a lattice? Which of the following graphs are lattice and why? Ans:  Let (L, ≤) be a poset. If each subset {x, y} consisting of any two elements of L, comprises a glb (I

Help, how long would it take if a submarine if it goes 3 feet per minute to...

how long would it take if a submarine if it goes 3 feet per minute to get to 20000 answer

complex number z, For complex number z, the minimum value of |z| + |z - co...

For complex number z, the minimum value of |z| + |z - cosa - i sina|+|z - 2(cosa + i sina )| is..? Solution) |z| + |z-(e^ia)| + |z-2(e^ia)| we see.....oigin , e^ia , 2e^ia ,  f

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