# Exponential Growth Calculator

Enter the value that you want to calculate exponential growth..

 Enter initial value (x0): Enter growth/decay rate %(r) : Enter time (t):
 Value at time t (x(t)):

## Math Calculators

### Exponential Growth & Decay Calculator

Our free online exponential growth calculator computes exponential growth or decay rates with the help parameters like time period (t), growth rate (r), & Initial value (x) and exponential growth formula.

Exponential Growth Rate Formula

x(t) = x0 × (1 + r) power of (t)

x(t) = x0 × (1 + r) t

x(t) is the value at time t.

x0 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.

## Example

x0 = 50

r = 4% = 0.04

t = 90 hours

x(t) = x0 × (1 + r) t = 50×(1+0.04)90 = 1706

## Exponential Growth Calculator

Discover the power of exponential growth and decay with our user-friendly calculator. Perfect for financial forecasting, population studies, and more, this tool calculates future values using the exponential growth formula.

#### How to Use the Exponential Growth Calculator

1. Enter the initial value (x0) of the quantity.
2. Input the growth rate (r), expressed as a percentage.
3. Specify the time period (t) over which the growth occurs.
4. Get the value at time t (x(t)) calculated instantly.

#### Exponential Growth Formula

The formula used for calculating exponential growth is:

$x(t) = x_0 \times (1 + r)^t$

• $$x(t)$$ 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.

Use the formula $$x(t) = x_0 \times (1 + r)^t$$, where $$x_0$$ is the initial value, $$r$$ is the growth rate, and $$t$$ is the time period.
The inverse of 3 modulo 7 is the number which, when multiplied by 3 and taken modulo 7, yields 1. In this case, it's 5, since $$(3 \times 5) \mod 7 = 1$$.