Element X is a radioactive isotope such that every 75 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 920 grams, how much of the element would remain after 3 years, to the nearest whole number? Answer:

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Element  X is a radioactive isotope such that every 75 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 920 grams, how much of the element would remain after 3 years, to the nearest whole number? Answer:

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Determine half-life of Element X: Determine the half-life of Element X. The half-life of Element X is given as 75 years. This means that every 75 years, the mass of Element X is reduced by half.Calculate number of half-lives: Calculate the number of half-lives that occur in 3 years. Since the half-life is 75 years, we need to find out how many 75-year periods fit into 3 years. This is done by dividing 3 by 75. Number of half-lives = 3 years / 75 years = 0.04 half-lives (approximately).Use exponential decay formula: Use the exponential decay formula to find the remaining mass. The formula for exponential decay is: Final mass = Initial mass * (1/2)^(Number of half-lives) We will use the number of half-lives calculated in Step 2 to find the remaining mass after 3 years.Plug values into formula: Plug the values into the exponential decay formula. Final mass = 920 grams * (1/2)^(0.04) To calculate this, we need to evaluate (1/2)^(0.04).Calculate (1/2)^(0.04): Calculate (1/2)^(0.04). Using a calculator, we find that (1/2)^(0.04) is approximately 0.971.Multiply initial mass: Multiply the initial mass by the decay factor to find the final mass. Final mass = 920 grams * 0.971 Final mass ≈ 893.32 gramsRound final mass: Round the final mass to the nearest whole number. The final mass of Element X after 3 years, rounded to the nearest whole number, is approximately 893 grams.

Element $\mathrm{X}$ is a radioactive isotope such that every $75$ years, its mass decreases by half. Given that the initial mass of a sample of Element X is $920$ grams, how much of the element would remain after $3$ years, to the nearest whole number? $\newline$ Answer:

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Element $\mathrm{X}$ is a radioactive isotope such that every $75$ years, its mass decreases by half. Given that the initial mass of a sample of Element X is $920$ grams, how much of the element would remain after $3$ years, to the nearest whole number? $\newline$ Answer: