Linear and Exponential Growth

Exponential growth:

Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value. In the case of a discrete domain of definition with equal intervals it is also called geometric growth or geometric decay. The exponential growth model is also known as the Malthusian growth mode.

Linear growth:

This function represents a process of growth which always adds the same relative amount. In this, the most simple case, it adds one unit, whether that unit is from 0 to 1, or from 1000 to 1001. When you connect the dots, you get a straight line, this type of function is said to be linear. With a linear function, Arithmetic proportion is always represented by a linear function.

Linear and Exponential Growth

Formula for linear growth

As we already studied, a linear growth is the addition of same relative amount of the previous. The growth of linear function can be given as, y = mx + b

The exponential growth formula:

F(t) = a.e^kt where

K > 0

A = the initial initial amount of a substance, and

T = the number of years (or any other unit of time ) elapsed since a given starting point.

When dealing with the time n required to double or half the amount of a substance,e the model for exponential growth and decay can be written as f(t) = a(2)^1/n and f(t) = a`(1/2)` ^`1/n` . respectively.

Hope you liked the above explanation. Please leave your comments, if you have any doubts.