Concept:
The age of the Earth has been determined using radiometric dating of rocks and meteorites.
The accepted age is approximately
\[
\boxed{4.54\text{ to }4.6\ \text{billion years}.}
\]
Step 1: Understand radiometric dating.
Scientists determine the Earth's age by studying the decay of radioactive isotopes such as Uranium and Lead in the oldest rocks and meteorites.
Step 2: Recall the accepted age.
The approximate age is
\[
\boxed{4.6\ \text{billion years}.}
\]
Therefore, the correct option is
\[
\boxed{(C)\;4.6\text{ billion years}.}
\]