A superhero is rendered powerless when exposed to 30 or more grams of a certain element. A 650 year old rock that originally contained 200 grams of this element was recently stolen from a rock museum by the superhero's nemesis. The half-life of the element is known to be 250 years. a) How many grams of the element are still contained in the stolen rock? b) For how many years can this rock be used by the superhero's nemesis to render the superhero powerless? a) The stolen rock still contains about $\square$ grams of the element. (Do not round until the final answer. Then round to two decimal places as needed.) b) The stolen rock can be used to render the superhero powerless for approximately another $\square$ years. (Round to the nearest whole number as needed.)

Step 1 ：Given that the initial amount of the element in the stolen rock is \(P = 200\) grams, the time that has passed since the rock was stolen is \(t = 650\) years, and the half-life of the element is \(h = 250\) years, we can use the formula for exponential decay, \(A = P * (1/2)^{t/h}\), to find out how many grams of the element are still contained in the stolen rock.

Step 2 ：Substituting the given values into the formula, we get \(A = 200 * (1/2)^{650/250} = 200 * (1/2)^{2.6} \approx 35.36\) grams.

Step 3 ：\(\boxed{35.36}\) grams of the element are still contained in the stolen rock.

Step 4 ：To find out for how many years the rock can be used to render the superhero powerless, we need to solve the equation \(A = P * (1/2)^{t/h}\) for \(t\), where \(A\) is the final amount (30 grams), \(P\) is the initial amount (35.36 grams), and \(h\) is the half-life (250 years).

Step 5 ：Solving this equation for \(t\), we get \(t = 250 * \log_{2}(35.36/30) \approx 57\) years.

Step 6 ：The stolen rock can be used to render the superhero powerless for approximately another \(\boxed{57}\) years.