Drug liver elimination

The patient was given the drug, and the measured liver concentration was t hours after administration: c (t) = -0.025 t² + 1.8t. When will the liver product be eliminated entirely?

Final Answer:

t =  72

Step-by-step explanation:

$$\begin{gathered} c(t)=-0,025t^2+1,8t \\ c(t)=0 \\ -0,025t^2+1,8t=0 \\ -0,025t^2+1,8t=0 \\ -0.025t^2+1.8t=0 \\ 0.025t^2-1.8t=0 \\ a=0.025;b=-1.8;c=-0 \\ D=b^2-4ac=1.8^2-4\cdot 0.025\cdot -0=3.24 \\ D>0 \\ {t}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{1.8\pm \sqrt{3.24}}{0.05}=36\pm \sqrt{1296} \\ {t}_{1,2}=36\pm 36 \\ {t}_1=72 \\ {t}_2=0 \\ t=t_1=72 \end{gathered}$$

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