# Exponential Growth Formula

Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function’s current value, resulting in its growth with time being an exponential function.

Formula of Exponential Growth

\[\large P(t)=P_{0}e^{rt}\]

Where:

t = time (number of periods)

P(t) = the amount of some quantity at time t

$P_{0}$ = initial amount at time t = 0

r = the growth rate

**Solved Examples**

**Question 1: **Suppose that the population of a certain country grows at an annual rate of 4 %. If the current population is 5 million, what will the population be in 15 years?

**Solution:**

Given

$P_{0}$ = 5

r = 0.04

t=15 years

Exponential growth,

$\large P(t)=P_{0}e^{rt}$

$P(15)$ = 5 $\times e^{0.04 \times 15}$

$P(15)$ = 9.11059 million

The population in 15 years is 9.11059 million