Final answer:
The given LTI system with the given input and impulse response is causal.
Step-by-step explanation:
The given LTI (Linear Time-Invariant) system can be analyzed to determine if it is causal or not. A system is considered causal if its output at any time depends only on the present and past values of the input.
In this case, the input function is x(t) = e-αᵗu(t), where α is a constant and u(t) is the unit step function. The impulse response of the system is h(t) = eβᵗu(−t), where β is another constant.
If we consider the time dependence of both the input and impulse response, we can see that the output of the system at any given time depends on the past and present values of the input. Therefore, the given system is causal.