The half-life of Radium- 226 is 1590 years. If a sample contains 400 mg, how many mg will remain after 4000 years? $\mathrm{mg}$ Give your answer accurate to at least 2 decimal places. Question Hetp: rindeo 4 wideo 2 Submit Question

Step 1 ：The half-life of a substance is the time it takes for half of the substance to decay. This is an exponential decay problem, and the formula for exponential decay is: \(N = N0 * (1/2)^{t/h}\) where: \(N\) is the final amount of the substance, \(N0\) is the initial amount of the substance, \(t\) is the time that has passed, \(h\) is the half-life of the substance.

Step 2 ：In this case, \(N0\) is 400 mg, \(t\) is 4000 years, and \(h\) is 1590 years. We can substitute these values into the formula to find \(N\), the amount of the substance that will remain after 4000 years.

Step 3 ：Substituting the given values into the formula, we get: \(N = 400 * (1/2)^{4000/1590}\)

Step 4 ：Solving the above expression, we get \(N = 69.94421915270917\)

Step 5 ：Rounding to two decimal places, the final answer is: \(\boxed{69.94}\) mg