Question

Consider the following scenario: A sample of radioactive material has a decay constant of 0.04 per hour. If there are initially 500 grams of the material, how much will remain after 3 hours? Choose the correct formula. (1 point)
Responses

y=3(0.96)^500
y is equal to 3 times 0 point 9 6 to the 500th power

y=500(0.96)^3
y is equal to 500 times 0 point 9 6 cubed

y=3(0.04)^500
y is equal to 3 times 0 point 0 4 to the 500th power

y=500(0.04)^3

Answer 1

To determine how much of the radioactive material will remain after 3 hours, we can use the formula for exponential decay:

\[
y = y_0 e^{-\lambda t}
\]

where:
- \( y \) is the amount of material remaining,
- \( y_0 \) is the initial amount of material (500 grams in this case),
- \( \lambda \) is the decay constant (0.04 per hour),
- \( t \) is the time elapsed (3 hours here).

We can also rewrite the exponential decay formula using a base of \( (1 - \text{decay rate}) \):

\[
y = y_0 (1 - r)^t
\]

where \( r = \text{decay constant} \).

In this case, the decay rate is:

\[
1 - r = 1 - 0.04 = 0.96
\]

So, after 3 hours, the calculation would become:

\[
y = 500(0.96)^3
\]

Therefore, the correct formula from your options is:

**y = 500(0.96)^3**

This means that significantly false interpretations (using a base of decay constant directly) have been eliminated in the options. Thus, this is the answer.