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)):

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.

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 \( (3 \times 5) \mod 7 = 1 \).