Exponential Growth Calculator

How to Calculate Exponential Growth

Exponential growth is a mathematical concept that describes how quantities increase over time at a rate proportional to the current amount. This process is common in many natural and scientific phenomena, such as population growth, compound interest, and the spread of diseases.

Formula

The general formula for exponential growth is:

\[ A = A_0 (1 + r)^t \]

Where:

• A is the final value after growth
• A₀ is the initial value
• r is the growth rate (as a decimal)
• t is the time elapsed

Calculation Steps

1. Identify the initial value (A₀), growth rate (r), and time (t).
2. Convert the growth rate to a decimal if it's given as a percentage.
3. Add the growth rate to 1: (1 + r).
4. Raise (1 + r) to the power of t.
5. Multiply the result by the initial value (A₀).
6. The result is the final value after growth.

Example

Let's calculate the exponential growth of an investment with an initial amount of $1000, growing at a rate of 5% per year, after 3 years:

1. Initial value (A₀) = $1000, Growth rate (r) = 5% = 0.05, Time (t) = 3 years
2. A = 1000 (1 + 0.05)³
3. A = 1000 (1.05)³
4. A = 1000 × 1.157625
5. A = $1157.63

After 3 years, the investment has grown to $1157.63.

Visual Representation

This diagram illustrates the exponential growth of the investment over 3 years, showing how the amount increases more rapidly as time progresses due to compound growth.