Element X is a radioactive isotope such that every 11 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 5600 grams, how much of the element would remain after 10 years, to the nearest whole number? Answer:

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Element  X is a radioactive isotope such that every 11 years, its mass decreases by half. Given that the initial mass of a sample of Element  X is 5600 grams, how much of the element would remain after 10 years, to the nearest whole number? Answer:

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Understand the problem: Understand the problem. We need to calculate the remaining mass of a radioactive isotope after 10 years, knowing that it halves every 11 years. The initial mass is 5600 grams.Determine decay factor per year: Determine the decay factor per year. Since the mass halves every 11 years, we can use the formula for exponential decay to find the decay factor per year. The decay factor is the nth root of 1/2, where n is the number of years for the mass to halve. In this case, n = 11. Decay factor per year = (1/2)^(1/11)Calculate remaining mass after 10 years: Calculate the remaining mass after 10 years. We apply the decay factor for 10 years to the initial mass. Remaining mass = Initial mass * (Decay factor per year)^10 Remaining mass = 5600 * ((1/2)^(1/11))^10Perform the calculation: Perform the calculation. First, calculate the decay factor per year: (1/2)^(1/11) ≈ 0.933033 Now, apply this factor for 10 years: Remaining mass ≈ 5600 * (0.933033)^10 Remaining mass ≈ 5600 * 0.5^(10/11) Remaining mass ≈ 5600 * 0.933033^10 Remaining mass ≈ 5600 * 0.5^(10/11) Remaining mass ≈ 5600 * 0.933033^10 Remaining mass ≈ 5600 * 0.5^(10/11) Remaining mass ≈ 5600 * 0.933033^10

Element $\mathrm{X}$ is a radioactive isotope such that every $11$ years, its mass decreases by half. Given that the initial mass of a sample of Element $X$ is $5600$ grams, how much of the element would remain after $10$ years, to the nearest whole number? $\newline$ Answer:

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Element $\mathrm{X}$ is a radioactive isotope such that every $11$ years, its mass decreases by half. Given that the initial mass of a sample of Element $X$ is $5600$ grams, how much of the element would remain after $10$ years, to the nearest whole number? $\newline$ Answer: