How do scientists know how old whale sharks can live?

There are annual bands in a whale shark's vertebrae which allow for both age and growth rates to be determined. A technique like radiocarbon dating can be used here. It seems that cold war testing of nuclear devices helped to accurately determine these values, because of the whale sharks' uptake of particular isotopes.

Whale sharks can live anywhere from 70 to 100 years.

Even though above ground bomb trials had ceased, plants and animals had already accumulated Carbon 14 in their bodies. While it was not necessarily detrimental to their health, the Carbon 14 left a lasting mark – one that can still be seen by scientists today. Sharks alive during bomb trials incorporated Carbon 14 into their tissues, including their vertebrae. Scientists can use this elevated amount of Carbon 14 laid down in vertebrae as a chemical marker, allowing them to estimate the ages of older sharks.

https://oceanbites.org/how-scientists-use-our-nuclear-past-to-understand-whale-shark-life-history/