A researcher is monitoring the concentration of a specialized catalyst, PPP mg/L, within a chemical bioreactor. The concentration ttt minutes after the reaction commences is modelled by the equation
P=480e0.12t2e0.12t+3,t≥0, t∈R P = \frac{480e^{0.12t}}{2e^{0.12t} + 3}, \quad t \ge 0, \ t \in \mathbb{R} P=2e0.12t+3480e0.12t,t≥0, t∈RAccording to this model:
Determine the concentration of the catalyst at the instant the reaction begins.
Calculate the time ttt at which the concentration reaches 160 mg/L, giving your answer to 2 decimal places.
Explain why, according to this model, the concentration of the catalyst can never reach 250 mg/L.
