Question

What is the exponential growth formula?

Answer 1

Hint: An exponential function is a function which is of the form $g\left( x \right)=a{{b}^{x}}$ where $a,b$ a positive real number is and $x$ is an exponent. Exponential growth is when the quantity is increased over time. It increases very slowly at first and then there is a rapid change. It is used to calculate the growth which is not so constant and has a curve growth.

Complete step-by-step answer:
The Exponential growth formula of a variable $x$ whose growth is in the rate $r$ as the time $t$ goes on in many discrete intervals is given as below:
${{x}_{t}}={{x}_{0}}{{\left( 1+r \right)}^{t}}$
Where,
${{x}_{0}}$ Is the value of $x$ at time 0 or at starting of the growth when the time is 0
The formula of exponential growth states that the quantity increases very slowly at first but after some time the growth in it becomes very rapid. As time passes out the rate of growth also becomes faster. This rapid growth is known as “Exponential increase”.

Note: Exponential Growth is used in many real-world problems specially to know the growth or decay of a bacteria or virus. It is also used to find the growth or decline in population of any species such as humans. It is also used in Compound interest as it provides a constant interest rate which has exponential growth to the capital. In the current scenario it is used to calculate the rate of percent suffering from corona virus which is an exponential growth as it is increasing day by day rapidly.