the half - life of a radioactive kind of barium is 3 minutes. if you start with 9,152 grams of it, how much…

Explanation:

Step1: Calculate the number of half - lives

The half - life is 3 minutes and the time elapsed is 12 minutes. The number of half - lives $n=\frac{12}{3}=4$.

Step2: Use the radioactive decay formula

The formula for radioactive decay is $A = A_0\times(\frac{1}{2})^n$, where $A_0$ is the initial amount and $n$ is the number of half - lives. Here, $A_0 = 9152$ grams and $n = 4$. So $A=9152\times(\frac{1}{2})^4$.

Step3: Calculate the remaining amount

First, $(\frac{1}{2})^4=\frac{1}{16}$. Then $A = 9152\times\frac{1}{16}=572$.

Answer:

572