Energy
Energy of the equation $ e^{-2t}u(t) $ is given by the formula:
$ E = \int_{t_1}^{t_2} \! e^{-4t}\ dt $.
where t1 and t2 are 0 and ∞ respectively.
The solution to this integral is 1/4.
Power
Power of the equation $ e^{-2t}u(t) $ is 0 because the energy of the signal is < ∞