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 is $A = A_0\times\left(\frac{1}{2}\right)^n$, where $A_0$ is the initial amount, $n$ is the number of half - lives, and $A$ is the final amount.

Step2: Substitute values

Given $A_0 = 115$ grams and $n = 5$. Substitute into the formula: $A=115\times\left(\frac{1}{2}\right)^5$.

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

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

Step4: Calculate final amount

$A = 115\times\frac{1}{32}=\frac{115}{32}=3.59375$.

Step5: Round to nearest gram

Rounding $3.59375$ to the nearest gram gives $4$ grams.

Answer:

4 grams