the half - life of a radioactive kind of cerium is 32 days. how much will be left after 160 days, if you…

Explanation:

Step1: Calculate number of half - lives

The number of half - lives $n=\frac{160}{32}=5$.

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, $A_0 = 57728$ grams and $n = 5$. So $A=57728\times(\frac{1}{2})^5$.

Step3: Calculate the remaining amount

$(\frac{1}{2})^5=\frac{1}{32}$, and $A = 57728\times\frac{1}{32}=1804$ grams.

Answer:

1804