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# Exponential Growth Calculator

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.

The results are displayed as a chart and a table of quantities on a new page.

 Exponential Growth Calculator Enter data for three of the first four fields. The calculator solves the fourth. Initial Quantity Final Quantity (Must be >Initial Quantity) Exponential Growth Rate (ex: enter 5 for 5%): % Elapsed Time: Maximum t: Increment t Value: Chart Height (pixels): Chart Width (pixels):
 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 Decay 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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