The half-life of a particular radioactive substance is 1 year. If you started with 40 grams of this substance, how much of it would remain after 3 years? Remaining Amount = $$ I(1-r)^{t} $$ [?] grams Round your answer to the nearest whole number.

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To determine the remaining amount of the radioactive substance after 3 years, we'll use the given formula:

$$
\text{Remaining Amount} = I(1 - r)^t
$$

**Where:**
- $$ I = 40 $$ grams (initial amount)
- $$ r $$ is the decay rate
- $$ t = 3 $$ years (time elapsed)

### Step 1: Determine the Decay Rate ($$ r $$)
Since the half-life is 1 year, after each year, half of the substance remains. This means:

$$
(1 - r) = \frac{1}{2}
$$

Solving for $$ r $$:

$$
r = 1 - \frac{1}{2} = \frac{1}{2}
$$

### Step 2: Calculate the Remaining Amount
Plugging the values into the formula:

$$
\text{Remaining Amount} = 40 \left(\frac{1}{2}\right)^3 = 40 \times \frac{1}{8} = 5 \text{ grams}
$$

### Final Answer
**5 grams** of the substance will remain after 3 years.
After 3 years, 5 grams of the substance remain.

The half-life of a particular radioactive substance is 1 year. If you started with 40 grams of this substance, how much of it would remain after 3 years? Remaining Amount = \( I(1-r)^{t} \) [?] grams Round your answer to the nearest whole number.

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