Final answer:
The rock is 3.6 billion years old because it has gone through three half-lives (as it now contains 1/8 of the original amount of the isotope), and each half-life is 1.2 billion years long. The correct option is A.
Step-by-step explanation:
To find out how many years old the rock is, we need to determine how many half-lives have passed given that the rock originally had 10 grams of a radioactive isotope and now has 1.25 grams. The half-life of the isotope is given as 1.2 billion years.
We use the formula for exponential decay, which states that the remaining amount of a radioactive isotope is equal to the initial amount times one-half to the power of the number of half-lives that have passed (N = N0 * (1/2)t). According to the question, only 1.25 grams of the isotope remain from an original 10 grams.
This represents an eighth of the original amount (since 10 divided by 1.25 equals 8), which corresponds to three half-lives (because (1/2)3 equals 1/8). Therefore, the rock has gone through three half-lives. To find the total age of the rock, we multiply the number of half-lives by the length of one half-life: 3 half-lives * 1.2 billion years/half-life = 3.6 billion years.
Hence, the correct answer is A.