the amount of radioactive element remaining, r, in a 100 - mg sample after d days is represented using the…

Answer:

B. 12.94%

Explanation:

Step1: Recall exponential - decay formula

The general form of an exponential - decay formula is $r = a(1 - r_0)^d$, where $a$ is the initial amount, $r_0$ is the rate of decay per time - unit, and $d$ is the number of time - units. The given formula is $r = 100(\frac{1}{2})^{\frac{d}{5}}$. We can rewrite it in the general form. Let's first rewrite $(\frac{1}{2})^{\frac{d}{5}}$ as $( (\frac{1}{2})^{\frac{1}{5}})^d$. Calculate $(\frac{1}{2})^{\frac{1}{5}}=\sqrt[5]{\frac{1}{2}}\approx0.8706$.

Step2: Find the decay rate

Since $r = a(1 - r_0)^d$ and $r = 100\times0.8706^d$, then $1 - r_0=0.8706$. Solving for $r_0$, we get $r_0 = 1 - 0.8706=0.1294$. Converting $r_0$ to a percentage, we multiply by 100. So the daily percent of decrease is $12.94%$.