Question

La concentración de cierto calmante suministrado mediante suero, varía en su efectividad en el tiempo según la siguiente función, C(t)=−t2+6t donde C es la concentración del calmante en el suero medida en milígramos por litro para que haga efecto durante t horas. ¿En que instante la concentración es de 8 milígramos por litro?

Answer 1

Answer: The concentration will be 8 milligrams per liter at 2 hours and 4 hours.

Step-by-step explanation:

GIven: The concentration of a certain painkiller supplied by serum varies in its effectiveness over time according to the following function, $C (t) = - t^2 + 6t$ where C is the concentration of the painkiller in the serum measured in milligrams per liter so that it takes effect during t hours.

Put C(t)=8, then we get

$8=-t^2+6t\\\\\Rightarrow\ t^2-6t+8=0\\\\\Rightarrow\ t^2-2t-4t+8=0\\\\\Rightarrow\ t(t-2)-4(t-2)=0\\\\\Rightarrow\ (t-2)(t-4)=0\\\\\Rightarrow\ t=2,4$

At t=2, $C(t)=-(2)^2+6(2)=-4+12=8$

At t=4, $C(t)=-(4)^2+6(4)=-16+24=8$

Hence, the concentration will be 8 milligrams per liter at 2 hours and  4 hours.