Exponential growth and Decay model:

If  is a differentiable function of  such that  and  for some constant , then .

 is the initial value of  and  is the proportional constant.

Exponential growth occurs when , and exponential decay occurs when .

The initial quantity is .

The isotope  has half life .

When  is  and  is .

.

Substitute  in .

.

When , .

.

When , .

.

Amount after : .

Amount after : .