Growth Rate Exponential

The mathematical function growth rate is proportional to current value function is called the exponential growth. Geometric growth is another form of exponential growth when equal intervals with discrete domain. Malthusian growth model is another name of exponential growth. Exponential growth is used in economics, computer technology and investment. It is evaluated by using exponential function.

 

Growth rate

 

Basic formula for exponential growth rate:

                 If x (t) = a.bt/T when the quantity x depends on time’t’. Here constant value is 'a' and it is denoted the 'x' initial value that is x (0) = a. Positive growth factor is constant 'b and the time is increased by x (t + Τ) = x (t)* b. The x is exponential growth when Τ > 0 and b > 1. The x is exponential decay when Τ < 0, b < 1 or Τ > 0 and 0 < b < 1.

                The same growth rate is represented by dimensionless non negative number and time amount as (b, T). This growth rate is related with T and log b in proportional. The non zero time is estimate the growth rate when b is not equal to one. This method has dimensionless positive number. The differential equation is separate the variables.

               The above figure is the example for exponential growth rate.

Parameters for growth rate:

  • The growth frequency is growth constant. It is denoted as K and estimate by factor. Logarithmic return, continuously compounded return or force of interest is another name of growth constant.
  • The time taken for growing is e-folding time. It is estimated by factor e.
  • The time taken for double the value is doubling time(T).
  • The period p has increased percent r.

 

             The growth rate has doubling time. It is calculated by popular approximated method.The rule of 70 is used for finding the exponential growth rate. The linear growth rate is overcome by exponential growth but it has faster growth rate.