# Exponential Graphs
=> differenciation.gmi You should understand differentiation before reading this section
Exponential graphs are those in the form of y = k^(x)
they should look like this:
y
|
|                  |
|                  |   
|                  |
|                 |
|                 |
|                |
|              _- 
|         ___-- 
|---------___________ x
As you can see, the line curves upwards, increasing in gradient costantly.
It's also interesting to note that all exponential graphs (without a specified y intercept), intersect y at 1 as n^0 === 1
If you draw the gradient graph of an exponential, you get another exponential graph, they are usually slightly different to the original graph, 
for instance, the gradient graph of 2^x is slightly shallower than 2^x 
and the gradient graph of 3^x is slightly steeper than 3^x,
As you can see, the gradient graph and initial graph must cross at a certain value between 2 and 3
that value is about 2.718, the gradient graph 2.718^x is exactly the same as 2.718^x, we call this value e. 
Similar to pi, the number e actually goes on forever, I just rounded it to 2.718, the first 10 digits are 2.718281828.
So e is a special number because if you differenciate it, you get the same value:
```
y     = e^x
dy/dx = e^x

y     = e^kx
dy/dx = ke^kx
```