Answer:
4.4 billion years
Explanation:
The decay of Uranium-238 to lead is a first-order radioactive decay process, and the amount of remaining Uranium-238 after time t can be modeled by the exponential decay formula:N(t) = N0 * e^(-λt)where N0 is the initial amount of Uranium-238, N(t) is the remaining amount after time t, and λ is the decay constant.The half-life of Uranium-238 is 4.468 billion years, which means that the decay constant can be calculated as:λ = ln(2) / t1/2 = ln(2) / (4.468 * 10^9 years) ≈ 1.55125 x 10^-10 years^-1We are given that 49.7% of the original Uranium-238 remains, which means that 50.3% has decayed. Therefore, the ratio of remaining Uranium-238 to original Uranium-238 is:N(t) / N0 = 0.497Taking the natural logarithm of both sides of the equation and solving for t, we get:ln(N(t) / N0) = -λtt = -ln(N(t) / N0) / λPlugging in the given values, we get:t = -ln(0.497) / (1.55125 x 10^-10 years^-1) ≈ 4.40 billion yearsTherefore, the age of the Moon rock is approximately 4.40 billion years. Note that we should round the answer to two significant digits because the given data only has two significant digits. So, the final answer is:t ≈ 4.4 billion years.