Enter an initial value, growth rate percent, and total time into the calculator below to determine the total exponential growth at the given time.
- Calculate a final value given the initial value, growth rate, and time.
- Calculate the initial value given the final value, growth rate, and time.
- Calculate the growth rate given the final value, initial value, and time.
- Calculate the time given the initial value, final value, and growth rate.
Exponential Growth Formula
The following formula is used by the calculator above to determine the exponential growth of a value.
x(t) = x0 × (1 + r)^t
- Where x(t) is the final value after time t
- x0 is the initial value
- r is the rate of growth in percent
- and t is the total time
Exponential Growth Definition
Exponential growth is defined as the growth of an object or asset that is described or can be modeled by an exponential function like the one above. Exponential functions grow “exponentially” with each step forward.
How to calculate exponential growth?
The following example is a step-by-step guide on determining the total value of a number after some time of exponential growth.
- First, we must determine the initial value. For this example, we will assume we are looking at an investment going through exponential growth through interest. Let’s assume a value of $1,000.00.
- The next step is the determine the growth rate r, this would be the interest per time step, so let’s assume interest per month. It will be 10%.
- The final step is to determine the total time that has passed. We will say 2 years or 24 months.
- Lastly, enter the information into the formula above to determine your answer.
Exponential growth is defined as the growth of an object or asset that is described or can be modeled by an exponential function.