 # Exponential Growth Formula

The exponential growth formula is used to express a function of exponential growth. To recall, 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. In other words, when the growth of a function increases rapidly in relation to the increase in the total number, then it is exponential.

## Formula of Exponential Growth

 P(t) = P0 ert

Where,

• t = time (number of periods)
• P(t) = the amount of some quantity at time t
• P0 = initial amount at time t = 0
• r = the growth rate
• e = Euler’s number = 2.71828 (approx)

Also Check: Exponential Function Formula

### Solved Examples Using Exponential Growth Formula

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

P0 = 5

r = 4% = 0.04

t = 15 years

Exponential growth,

P(t) = P0 ert

P(15) = 5 × e0.04×15

Substituting Euler’s number,

P(15) = 9.11059 million

The population in 15 years will be 9.11059 million (approx).