C

Step 1: Analyze statement I:
All radioactive elements do indeed decay exponentially over time, which is characteristic of radioactive decay. This statement is true.

Step 2: Analyze statement II:
The half-life (or half lifetime) of a radioactive element is defined as the time required for half of the radioactive atoms in a sample to decay. This statement is true.

Step 3: Analyze statement III:
The age of the earth can be estimated using various radioactive dating techniques, such as uranium-lead dating, which relies on the predictable decays of radioactive isotopes. This statement is true.

Step 4: Analyze statement IV:
The half-life of a radioactive element is not equal to 50% of its average life period. The average life is a different concept that can be calculated but is not simply 50% of the half-life. Therefore, this statement is false.

Conclusion: Since statements I, II, and III are true, the correct option that includes all true statements is C: I, II and III.