Step 1: Principle of Radio Carbon Dating.
Radio carbon dating estimates the age of a specimen by measuring the amount of \( ^{14}C \) present relative to \( ^{12}C \). The decay of \( ^{14}C \) allows for the determination of the age of ancient specimens.
Step 2: Conclusion.
Thus, the correct answer is option (C).
Final Answer:
\[
\boxed{\text{(C) the amount of } ^{14}C \text{ to } ^{12}C \text{ still present}}
\]