This problem describes a classic example of exponential decay, where the amount of a radioactive substance decreases over time. The mass of the substance halves every 5 years, so the decay can be modeled using the following exponential decay formula:

$m(t) = m_0 \times \left( \frac{1}{2} \right)^{\frac{t}{T}}$

Where:

• $m(t)$ is the remaining mass after time $t$,
• $m_0$ is the initial mass (590 grams),
• $T$ is the half-life of the element (5 years),
• $t$ is the elapsed time (23 years).

Step-by-step solution:

1. The initial mass of the sample, $m_0$, is 590 grams.
2. The half-life, $T$, is 5 years.
3. The time elapsed, $t$, is 23 years.

Substituting these values into the formula:

$m(23) = 590 \times \left( \frac{1}{2} \right)^{\frac{23}{5}}$

Now, let's calculate the value of $m(23)$.After 23 years, the remaining mass of Element X would be approximately 24 grams.

Would you like any further details on this? Here are some related questions to expand on this concept:

1. How would the remaining mass change if the half-life were 10 years instead of 5?
2. What is the general formula for the mass of a radioactive substance after $n$ half-lives?
3. How long would it take for the mass to decay to 1 gram?
4. How can this exponential decay model be used in fields like carbon dating?
5. What happens to the mass of a substance if the time is less than the half-life?

Tip: Radioactive decay follows exponential patterns, which are common in nature and also appear in population growth and financial interest models.