Question

The amount of radioactive element remaining, r, in a 100-mg sample after d days is represented using the equation r=100="https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B2%7D%29%5E%20%20%5Cfrac%7Bd%7D%7B5%7D%20" id="TexFormula1" title="( \frac{1}{2})^ \frac{d}{5} " alt="( \frac{1}{2})^ \frac{d}{5} " align="absmiddle" class="latex-formula"> . What is the daily percent of decrease?
87.06%
12.94%
3.13%
10%

Answer 1

$\bf r=100\left( \frac{1}{2} \right)^{\frac{d}{5}}\\\\ -------------------------------\\\\ \textit{after 1 day how much remains?}\qquad \boxed{d=1}\qquad r=100\left( \frac{1}{2} \right)^{\frac{1}{5}} \\\\\\ r=100\left( \cfrac{1^{\frac{1}{5}}}{2^{\frac{1}{5}}} \right)\implies r=100\left( \cfrac{1}{\sqrt[5]{2}} \right)\implies r\approx 87.06 \\\\\\ \textit{used to be 100mg, it went down in 1 day to 87.06 or }12.94$

how much is 12.94 in percent of 100?  well, since is 100, is just 12.94%.