the half - life of a radioactive kind of lead is 3 hours. if you start with 48,320 grams of it, how much…

Explanation:

Step1: Calculate number of half - lives

The half - life is 3 hours and the time elapsed is 15 hours. The number of half - lives $n=\frac{15}{3}=5$.

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, $A_0 = 48320$ grams and $n = 5$. So $A=48320\times(\frac{1}{2})^5$.

Step3: Calculate the remaining amount

$(\frac{1}{2})^5=\frac{1}{32}$, and $A = 48320\times\frac{1}{32}=1510$.

Answer:

1510