Is it possible to make a mathematical function generator using Arduino?
You can generate arbitrary waveforms using either the built-in PWM and a low-pass filter or an external DAC.

You won't get more than 16-bits in PWM ( or AFAIK non-audio DAC with arduino libraries ), so your e^N function will be below your resolution for most of the cycle.

Alternatively, generate a saw-tooth and use an op-amp exponential function