Pancreatic islet β-cells respond to a bolus of glucose by secreting insulin, which in turn transiently elevates plasma insulin and which can be approximated by the signal: x(t) = e^(-0.1t) * u(t). Note that time t is in minutes.
a) Sketch (by hand) the continuous-time signal x(t) over the range -10 ≤ t ≤ 50 minutes. Be precise and clearly show axes tick marks and labels.
b) Determine the even and odd components of the signal.
c) Show that the total energy of x(t) is the sum of energies of its odd and even components.