# Time-to-diffuse "explodes"

How does a graph of time to diffuse as a function of distance look? In other words,

1. Use the equation T = x^{2 }/ 2D

2. put distance (x) on the x-axis

3. put time (T) on the y-axis

4. assume D = 0.00001 cm^{2}/sec

So, what does the graph look like? Remember, that **T = x ^{2 }/ 2D is a quadratic equation**, equivalent to y = ax

^{2}and so takes the shape of a parabola. In this case, the constant “a” is represented by the term 1/2D. Here is the graph, using D = 0.00001.

Notice that **as the distance increases a little, time increases a lot**. We say that:

- “time to diffuse increases with the square of distance”, or equivalently,
- “distance diffused increases with the square root of time”.

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