Solve for fraction remaining

The fraction remaining of a radioactive substance is the ratio of the final amount ($N$) to the initial amount ($N_0$). It can be calculated using the formula:

$$\text{Fraction remaining} = \frac{N}{N_0} = \left(\frac{1}{2}\right)^{n}$$

where:

• $N$ is the final amount of the substance remaining.
• $N_0$ is the initial amount of the substance.
• $n$ is the number of half-lives that have passed, calculated as $n = \frac{t}{T_{1/2}}$.
• $t$ is the total time elapsed.
• $T_{1/2}$ is the half-life of the substance.

Example:
A radioactive sample has a half-life of 5 years. What fraction of the original sample will remain after 15 years?