the half - life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to…

Explanation:

Step1: Identify decay formula

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

Step2: Substitute values

Given $A_0 = 185$ grams and $n = 5$. Substitute these values into the formula: $A=185\times(\frac{1}{2})^5$.

Step3: Calculate $(\frac{1}{2})^5$

$(\frac{1}{2})^5=\frac{1}{2\times2\times2\times2\times2}=\frac{1}{32}$.

Step4: Calculate the final amount

$A = 185\times\frac{1}{32}=\frac{185}{32}=5.78125$ grams.

Step5: Round to the nearest gram

Rounding $5.78125$ to the nearest gram gives $6$ grams.

Answer:

$6$ grams