Question Number 144502 by alcohol last updated on 26/Jun/21
$${it}\:{is}\:{known}\:{that}\:{after}\:{injecting}\:{the}\:\mathrm{1}^{{st}} \\ $$$${dosage}\:{of}\:{a}\:{drug}\:{in}\:{exactly}\:{hours} \\ $$$${p}\left({t}\right)=\begin{cases}{{Ae}^{−\frac{{t}}{\mathrm{24}}} ,\:\mathrm{0}\leqslant{t}\leqslant\mathrm{8}}\\{\left({A}+{Ae}^{−\frac{\mathrm{1}}{\mathrm{3}}} \right){e}^{−\left(\frac{{t}−\mathrm{8}}{\mathrm{24}}\right)} ,\:\mathrm{8}\:\leqslant\:{t}\leqslant\mathrm{24}}\end{cases} \\ $$$${A}\:{is}\:{the}\:{initial}\:{dosage}\:{at}\:{t}=\:\mathrm{0}{hours} \\ $$$$\left.{a}\right)\:{show}\:{that}\:{towards}\:{the}\:{application}\:{of} \\ $$$${the}\:{n}^{{th}} \:{dosage}\:,\:{the}\:{dosage}\:{remained}\:{in}\:{blood}\:{is} \\ $$$$\left(\frac{\mathrm{1}−{e}^{−\frac{\mathrm{1}}{{n}}} }{\mathrm{1}−{e}^{−\frac{\mathrm{1}}{\mathrm{3}}} }\right)×{A} \\ $$
Commented by ArielVyny last updated on 26/Jun/21
$${polytechnique}\:{yaounde}\: \\ $$$${use}\:{the}\:{expression}\:{of}\:{geometric}\:{series} \\ $$
Commented by puissant last updated on 07/Jul/21
$$\mathrm{yesss} \\ $$