The half-life of Radium-226 is 1590 years. If a sample contains $300 \mathrm{mg}$, how many mg will remain after 1000 years?
$\mathrm{mg}$
Give your answer accurate to at least 2 decimal places.

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. The formula for exponential decay is: \(A = A_0 * (1/2)^{t/h}\) where: \(A\) is the final amount of the substance, \(A_0\) is the initial amount of the substance, \(t\) is the time that has passed, and \(h\) is the half-life of the substance.

Step 2 ：In this case, \(A_0 = 300\) mg, \(t = 1000\) years, and \(h = 1590\) years. We can substitute these values into the formula to find \(A\).

Step 3 ：Substituting the given values into the formula, we get \(A = 300 * (1/2)^{1000/1590}\)

Step 4 ：Solving the above expression, we get \(A = 193.99664239329994\)

Step 5 ：Rounding to two decimal places, we get \(A = 193.99\)

Step 6 ：Final Answer: The amount of Radium-226 that will remain after 1000 years is approximately \(\boxed{193.99}\) mg.