how much of a radioactive kind of thorium will be left after 14,680 years if you start with 35,912 grams and…

Explanation:

Step1: Calculate number of half - lives

The number of half - lives $n=\frac{14680}{7340}=2$.

Step2: Use half - life 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, $A_0 = 35912$ grams and $n = 2$. So $A=35912\times(\frac{1}{2})^2$.

Step3: Calculate the remaining amount

$A = 35912\times\frac{1}{4}=8978$ grams.

Answer:

8978