Exponential growth/decay formula calculator online free

Exponential growth/decay formula*x*(*t*) = *x*_{0} × (1 + *r*)^{ t}

*x*(t) is the value at time t.

*x*_{0} is the initial value at time t=0.

r is the growth rate when r > 0 or decay rate when r < 0, in percent.

t is the time in discrete intervals and selected time units.

## Exponential growth calculator

Enter the initial value *x*_{0}, growth rate r and time interval t and press the *Calculate* button:

## Example

*x*_{0} = 50

*r* = 4% = 0.04

*t* = 90 hours

*x*(*t*) = *x*_{0}* *
× (1 + *r*)^{ t} = 50×(1+0.04)^{90} = 1706

## Definition

where *x*_{0} is the value of x at time 0. The growth of a bacterial colony is often used to illustrate it. One bacterium splits itself into two, each of which splits itself resulting in four, then eight, 16, 32, and so on. The rate of increase keeps increasing because it is proportional to the ever-increasing number of bacteria. Growth like this is observed in real-life activity or phenomena, such as the spread of virus infection, the growth of debt due to compound interest, and the spread of viral videos. In real cases, initial exponential growth often does not last forever, instead slowing down eventually due to upper limits caused by external factors and turning into logistic growth.

## Example graph

Graph of the exponential function (red) with the tangent (light blue dotted line) through the point 0/1

*Source: Wikipedia*

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