An element with mass 230 grams decays by 27.7% per minute. How much of the element is remaining after 8 minutes, to the nearest 1oth of a gram? Answer:

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An element with mass 230 grams decays by  27.7% per minute. How much of the element is remaining after 8 minutes, to the nearest 1oth of a gram? Answer:

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Understand and Determine Formula: Understand the problem and determine the formula to use. We know that the element decays by 27.7% per minute. This means that each minute, the element retains 100% - 27.7% = 72.3% of its mass from the previous minute. To find the remaining mass after 8 minutes, we will repeatedly apply the decay rate of 72.3%.Convert Percentage to Decimal: Convert the percentage to a decimal to use in calculations. 27.7% as a decimal is 0.277, so the remaining percentage as a decimal is 1 - 0.277 = 0.723.Calculate Remaining Mass (1 minute): Calculate the remaining mass after the first minute. Remaining mass after 1 minute = Initial mass * Remaining percentage Remaining mass after 1 minute = 230 grams * 0.723Apply Decay Process (8 minutes): Perform the calculation for the remaining mass after the first minute. Remaining mass after 1 minute = 230 * 0.723 = 166.29 gramsCalculate Remaining Mass (8 minutes): Apply the decay process for 8 minutes. Since the decay happens each minute, we need to multiply the remaining mass by 0.723 for each of the 8 minutes. Remaining mass after 8 minutes = 230 * (0.723)^8Perform Calculation (8 minutes): Calculate the remaining mass after 8 minutes. Remaining mass after 8 minutes = 230 * (0.723)^8Complete Calculation and Round: Perform the calculation for the remaining mass after 8 minutes. Remaining mass after 8 minutes = 230 * (0.723)^8 ≈ 230 * 0.100258Complete the calculation and round to the nearest 10th of a gram. Remaining mass after 8 minutes ≈ 230 * 0.100258 ≈ 23.05934 grams Rounded to the nearest 10th of a gram, the remaining mass is approximately 23.1 grams.

An element with mass $230$ grams decays by $27.7 \%$ per minute. How much of the element is remaining after $8$ minutes, to the nearest $1$ oth of a gram? $\newline$ Answer:

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An element with mass $230$ grams decays by $27.7 \%$ per minute. How much of the element is remaining after $8$ minutes, to the nearest $1$ oth of a gram? $\newline$ Answer: