Follow up question is its value determined by the weight of the metals they are comprised of, auction values or an estimated exchange rate?

Short answer? It varied, a lot.

Long answer, the denarius varied in weight, the initial denarius weighed around 6.8 grams, spent a lot of time just under 4 grams, went to about 2.6 grams for a time, and ended up around 3.4 grams. The silver content also fluctuated up and down. It was about 98% pure silver under Tiberius. But by the end of the third century it had been debased to 5% pure. As you can imagine a 4 gram coin of 98% silver was worth a lot more than a 2.6 gram coin of 5% silver.

It's also hard to draw direct comparisons between value today and two millennia ago. Different things had different comparative value. People spent a lot more of their money on food, and tended to own a lot less goods in general. So even the wide ranges I'm giving below should be take with more than a grain of salt.

In the late republic / early empire, a single denarius would account for a single unskilled workers daily pay. Depending on whether we try and draw equivalences between minimum wage, or purchase parity, it would be worth somewhere between $10 and $100.

By the second century the coin was smaller and only about 80% pure. And was worth about half (or less) of what it had been, so between $2 and $50.

By the middle of the third century it had been debased to literal pocket change, and was probably similar to a quarter, where it would require several to buy even a cheap beverage so like 10¢ to 25¢.

There was later attempts to reverse the inflationary spiral. So it regained some value, but it never got back up past the $1 to $10 range again.

The TLDR? Depending on time and place, somewhere between 10¢ and $100.