Mathematics, 22.02.2022 15:20 snoopyqueen2597
A radioactive substance decays exponentially. A scientist begins with 130 milligrams of a radioactive substance. After 30 hours, 65 mg of the substance remains. How many milligrams will remain after 56 hours?
Answers: 1
![f(x)=ab^x~\hspace{10em}\underline{f(x)=130b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} ~\hfill x&=30\\ f(x)&=65 \end{cases}\qquad \implies 65=130b^{30}\implies \cfrac{65}{130}=b^{30}\implies \cfrac{1}{2}=b^{30}](/tpl/images/2667/2891/07faf.png)
![\sqrt[30]{\cfrac{1}{2}}=b\implies \cfrac{\sqrt[30]{1}}{\sqrt[30]{2}}=b\implies \cfrac{1}{\sqrt[30]{2}}=b~\hfill \underline{f(x)=130\left( \cfrac{1}{\sqrt[30]{2}} \right)^x} \\\\[-0.35em] ~\dotfill\\\\ \textit{when x = 56, what is f(x)?}\qquad f(x)=130\left( \cfrac{1}{\sqrt[30]{2}} \right)^{56}\implies f(x)\approx 35.647](/tpl/images/2667/2891/5cc84.png)
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A radioactive substance decays exponentially. A scientist begins with 130 milligrams of a radioactiv...
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