Mathematics, 06.10.2019 22:00 juvie65
Aradioactive substance decays exponentially. a scientist begins with 170 milligrams of a radioactive substance. after 27 hours, 85 mg of the substance remains. how many milligrams will remain after 49 hours?
Answers: 2
![\bf A=P(1+r)^t\qquad \begin{cases} P=\textit{starting amount}\\ r=\textit{rate of change}\\ A=\textit{current amount}\\ t=\textit{elapsed time}\\ --------\\ P=170\\ t=27\\ A=85 \end{cases}\implies 85=170(1+r)^{27} \\\\\\ \cfrac{85}{170}=(1+r)^{27}\implies \sqrt[27]{\cfrac{1}{2}}=1+r\implies \boxed{\cfrac{1}{\sqrt[27]{2}}-1=r}\\\\ -----------------------------\\\\ A=170\left( 1+\cfrac{1}{\sqrt[27]{2}}-1 \right)^t \iff A=170\left( \cfrac{1}{\sqrt[27]{2}} \right)^t](/tpl/images/0295/1591/7877e.png)
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