The growth whose rate becomes ever more rapid in proportion to the growing total number is called as exponential growth. In other words the exponential growth is appears when the original quantity grow exponentially over the time. Exponential growth is denoted by $P(T)$. It can be find by substituting initial value, time and growth rate in below formula.

Exponential Growth Formula:
$P(t)$ = $P_{0} e^{rt}$.
Where,
$P_{t}$ is the amount of data at time(t),
$P_{0}$ is initial amount at time(t=0),
r is growth rate,
t is time.

## Examples of Exponential Growth

Some of the solved examples of exponential growth formula are given below:

Example 1: In a survey the population growth of a country is 5%(per year). The initial population is 7 million. Find the population in 15 years?
Solution:

Given
$P_{0}$ = 7 million
r = 0.05
t = 15

Using formula
$P(t)$ = $P_{0} e^{rt}$

$P(t)$ = $7\times e^{0.04\times 15}$

$P(t)$ = 12.754

The population in 15 years is 12.754 million.

Example 2: Let the population growth of a country is at an annual rate of 10%. The initial population is 11 million. Find the population in 20 years?
Solution:

Given
$P_{0}$ = 11 million
r = 0.10
t = 20

Using formula
$P(t)$ = $P_{0} e^{rt}$

$P(t)$ = $11\times e^{0.10\times 10}$

$P(t)$ = 81.279

The population in 20 years is 81.279 million.