# Exponential Growth Calculator and Grapher

An online calculator and grapher for exponential growth (increasing) functions of the form

a(t) = A er t

where A is the initial amount to model, r (positive) is the rate of increase and t is the time. Because the exponent r t is positive, the above function increases as the time t increases.
Exponential growth functions have various applications in electricity, physics, chemistry, eletricity, economics and many other fields. Therefore a thorough understanding of this class of functions is necessary for their proper applications.
One way to better understand exponential growth functions is to compare two or more of these functions with different parameters A and r. In order to understand the effect of each of the two parameters, we need to fix one of the parameters, r for example with r1 = r2, and assign different values to A1 and A2 which makes it easy to understand the effect of A.

## How to use the Exponential Growth Calculator and Grapher

The use of this grapher helps you understand the behaviour of exponential growth functions as time t increases by comparing several functions with different parameters. This calculator uses two functions of the exponential growth type where the parameters of each one may be set at values desired.
Enter the initial amount A1 and the rate of decrease r1 (positive) for the first function
a1(t) and the amount A2 and rate of decrease r2 (positive) for the second function a1(t) then press the button "Graph". Time t is entered as an interval of time starting from zero.
Start with small values (2, 5, ..) of the time interval and increase it to understand the behaviour of the function for small values of t, and then increase t to understand the behaviour of the same function for larger values of time.
Similarly for the parameters r1 and r2, start with small values (0.001, 0.02, 0.03,...) and increase them to understandt their effects on the behaviour of the function.

a1(t) = A1 er1 t :      A1 = r1 =
a2(t) = A2 er2 t :      A2 = r2 =
Time Interval = Seconds

Hover the mousse cursor on the graph to read the value of the time t and the y coordinate which is equal to the value of the function a(t).
Hover the mousse cursor on the top right of the graph to have the option of download the graph as a png file.

Exponential Functions.
Graph of Exponential Functions.