Exponential growth/decay calculator

Enter initial value (x0):  
Enter growth/decay rate (r): %
Enter time (t):  
   
Value at time t (x(t)):  

Exponential decay/growth is very useful in mathmatics. Exponential decay occurs when the growth rate is negative. Exponential growth in the same way occurs when the growth rate of the value of a mathematical function is proportional to the function's current value.

The formula for exponential growth of a variable x at the (positive or negative) growth rate r, as time t goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is xt = x0(1+r)t.

where x0 is the value of x at time 0. When the r is negative itis Exponential decay, when the r is positive, it is Exponential growth. For instance, The growth rate of r = 5% = 0.05, going from any integer value of time to the next integer causes x at the second time to be 1.05 times what it was at the previous time.

For instance, r = -0.5, the graph will be decreasing (decaying). each time t is increased by 1, xt decreases to one half of its previous value.

When r = 1, the graph will be growth. each time t is increased by 1, xt increases by a factor of 2.

The graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth.

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