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

         y = m. a^x

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 = ma^x is the x-th term in a Geometric Progression.

Figure 

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,

y_n      = A(1 + r)ⁿ       

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