Question

The amount of radioactive element remaining, r, in a 100-mg sample after d days is represented using the equation r=100
`( (1)/(2))^ (d)/(5)` . What is the daily percent of decrease?

87.06%
12.94%
3.13%
10%

Answer 1

its 12.94%

Explanation

Answer 2

`\bf r=100\left( (1)/(2) \right)^{(d)/(5)}\\\\ -------------------------------\\\\ \textit{after 1 day how much remains?}\qquad \boxed{d=1}\qquad r=100\left( (1)/(2) \right)^{(1)/(5)} \\\\\\ r=100\left( \cfrac{1^{(1)/(5)}}{2^{(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%.