Many dynamic processes can be approximated as an exponential decay. This applies to radioactive decay, some chemical reactions, ageing of LEDs etc. See https://en.wikipedia.org/wiki/Exponential_decay for more background.

Assume that the process starts with a normalised value of x(0) = 1, and it follows the following decay law:

x'(t) = - x(t) / tau

where x'(t) is the first derivative of x(t), and time constant tau is 2.

Write a function that returns the value x for a given input t. It should be able to deal with a vector input.