C

Step 1: Analyze Statement I:
All radioactive elements indeed undergo exponential decay with time. This means that the amount of the substance will decrease by a consistent percentage over equal time intervals. Thus, statement I is true.

Step 2: Analyze Statement II:
The half-life of a radioactive element is defined as the time required for half of the radioactive atoms in a sample to disintegrate, which is a correct statement. Therefore, statement II is also true.

Step 3: Analyze Statement III:
Radioactive dating, using isotopes with known half-lives, can determine the age of the Earth through the ratio of parent isotopes to daughter isotopes in geological samples. Hence, statement III is true.

Step 4: Analyze Statement IV:
The average life period (mean life) of a radioactive element is the expected lifetime of the particles, and the half-life is not 50% of this average life; rather, the relationship is such that the half-life is actually shorter than the average life. Therefore, statement IV is false.

Conclusion: The true statements are I, II, and III. Therefore, the correct answer is option C.