We are given a radioactive isotope with a half-life of 5 years. We are given an initial amount of 120 grams. We want to find the equation that determines the amount of material remaining, $y$, after $x$ years.

1. Problem Description

We are given a radioactive isotope with a half-life of 5 years. We are given an initial amount of 120 grams. We want to find the equation that determines the amount of material remaining, $y$, after $x$ years.

2. Solution Steps

The general formula for exponential decay (including radioactive decay) is

$y = A(1/2)^{t/T}$

where $y$ is the amount remaining after time $t$, $A$ is the initial amount, and $T$ is the half-life.

In this case, we have $A=120$ grams, $T = 5$ years, and $t = x$ years. Substituting these values into the formula, we get:

$y = 120(1/2)^{x/5}$

Therefore, the correct equation is $y = 120 \times (1/2)^{x/5}$.

3. Final Answer

$y = 120 \times (\frac{1}{2})^{\frac{x}{5}}$