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 =Â 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).
Comments