Automated Insulin Delivery Infusion (Biomedical Engineering)

In closed-loop biomedical devices, an automated artificial pancreas regulates blood glucose levels by computing active residual insulin in the patient's bloodstream before authorizing a micro-bolus injection.

The residual active insulin $I(t)$ (in Units) over elapsed time $t$ (in hours) since the last automated basal release valve activation is modeled by the composite saturation decay function:

1. Using composite limit techniques, evaluate $\lim_{t \to 0^+} I(t)$ to determine the instantaneous active insulin baseline at the exact instant the infusion valve opens.
2. If the control algorithm required a non-zero initial reference value of $10\text{ Units}$ to prevent a double-dose calculation error, verify whether the system meets this physiological baseline specification.