Final answer:
The decay rate for the exponentially decaying signal x(t) = 4e^-t/3 is -1/3, as it is the coefficient of t in the exponent and signifies a decrease over time.
Step-by-step explanation:
To calculate the decay rate for the exponentially decaying signal given by x(t) = 4e-t/3, we need to identify the term in the exponent associated with time (t). The general form for an exponential decay signal is x(t) = Ae‑λt, where λ is the decay constant. In the given equation, the decay constant λ corresponds to 1/3, as it is the coefficient of t in the exponent. Therefore, the decay rate is 1/3. However, it is conventional to give the decay rate as a negative because it signifies a decrease over time, which makes the correct decay rate ‑1/3.