A chemical reactor's internal pressure $P$, measured in kilopascals (kPa), increases over time $t$ (minutes) according to the model

$$P=\frac{3}{4}{t}^2+12,t\ge 0$$

A monitoring system tracks the pressure until it reaches a critical threshold of 39 kPa. The finite region $R$ in the first quadrant of the $t$-$P$ plane is bounded by the $P$-axis, the horizontal line $P=39$, and the curve representing the reactor's pressure.