A sample of a certain isotope takes 29 years to decay to half its original mass.

Choice A is correct. In the given function, $s\left(t\right)$ represents the approximate mass, in grams, of the sample that remains $t$ years after the sample starts to decay. It follows that the best interpretation of $s\left(87\right)=23$ is that approximately $23$ grams of the sample remains $87$ years after the sample starts to decay.

Choice B is incorrect. The mass of the sample has decreased by approximately $184-23$, or $161$, grams, not $23$ grams, $87$ years after the sample starts to decay.

Choice C is incorrect. The mass of the sample has decreased by approximately $78$ grams, not $87$ grams, $23$ years after the sample starts to decay.

Choice D is incorrect. This would be the best interpretation of $s\left(23\right)=87$, not $s\left(87\right)=23$.