The concentration CCC (in mg/L) of a chemical catalyst over time ttt (in minutes) is modeled by the function
C(t)=(2t−3)4e−2t,t≥1.5 C(t) = (2t - 3)^4 e^{-2t}, \quad t \ge 1.5 C(t)=(2t−3)4e−2t,t≥1.5Show that
C′(t)=A(2t−3)3(7−2t)e−2t C'(t) = A(2t - 3)^3 (7 - 2t) e^{-2t} C′(t)=A(2t−3)3(7−2t)e−2twhere A A\,A is a constant to be found.
Hence find the exact coordinates of the two stationary points on the curve with equation y=C(t)y = C(t)y=C(t).
A secondary reaction is modeled by the function HHH, defined by
H(t)=5C(t+0.5) H(t) = 5 C(t + 0.5) H(t)=5C(t+0.5)Find the coordinates of the maximum stationary point on the curve with equation y=H(t)y = H(t)y=H(t).
