# Exponential Growth Calculator and Chart Maker

The Exponential Growth Calculator evaluates the following continuous exponential growth function:

Where:

A(t) is the quantity at time t.

A0 is the initial quantity.

r is the exponential growth rate for each t time interval and r is > 0.

t is the total number of elapsed time intervals.

Maximum t through Chart Width (light gray/light yellow) are parameters for the chart of A(t) values.

Exponential Growth Calculator and Chart Maker
Enter data in three of the first four fields. The calculator solves the blank field.
Initial Quantity
Final Quantity (Must be < Initial Quantity)
Exponential Growth Rate (%):
Elapsed Time:
Maximum t:
Increment t Value:
Enter only numbers and decimal points in fields.

Computational Notes:

Initial Quantity calculation is:

$A{_{0}}&space;=&space;A(t)/e^{rt}$

Final Quantity calculation is:

$A(t)&space;=&space;A{_{0}}e^{rt}$

Exponential Growth Rate calculation is:

$r&space;=&space;\ln(A(t)/A{{_{0}}})/t$

Elapsed Time calculation is:

$t&space;=&space;\ln&space;(A(t)/A{_{0}})/r$

Half-life calculation is:

$t_{1/2}&space;=&space;t\ln&space;(2)&space;/&space;\ln(A_{0}/A(t){_{}})$

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