## 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

- Enter the initial value (
`x0`

) of the quantity. - Input the growth rate (
`r`

), expressed as a percentage. - Specify the time period (
`t`

) over which the growth occurs. - 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.

#### Frequently Asked Questions

- How do I calculate exponential growth?
- 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.
- What is exponential growth rate?
- The exponential growth rate is the rate at which a quantity increases over time in an exponential manner, typically expressed as a percentage.
- Is doubling exponential growth?
- Yes, doubling can be considered a form of exponential growth, especially when a quantity doubles over consistent time intervals.
- What is the inverse of 3 modulus 7?
- 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 \( (3 \times 5) \mod 7 = 1 \).