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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:

An element with mass 230230 grams decays by 27.7% 27.7 \% per minute. How much of the element is remaining after 88 minutes, to the nearest 11oth of a gram?\newlineAnswer:

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Full solution

Q. An element with mass 230230 grams decays by 27.7% 27.7 \% per minute. How much of the element is remaining after 88 minutes, to the nearest 11oth of a gram?\newlineAnswer:
  1. Understand and Determine Formula: Understand the problem and determine the formula to use.\newlineWe know that the element decays by 27.7%27.7\% per minute. This means that each minute, the element retains 100%−27.7%=72.3%100\% - 27.7\% = 72.3\% of its mass from the previous minute. To find the remaining mass after 88 minutes, we will repeatedly apply the decay rate of 72.3%72.3\%.
  2. Convert Percentage to Decimal: Convert the percentage to a decimal to use in calculations. 27.7%27.7\% as a decimal is 0.2770.277, so the remaining percentage as a decimal is 1−0.277=0.7231 - 0.277 = 0.723.
  3. Calculate Remaining Mass (11 minute): Calculate the remaining mass after the first minute.\newlineRemaining mass after 11 minute = Initial mass ×\times Remaining percentage\newlineRemaining mass after 11 minute = 230230 grams ×0.723\times 0.723
  4. Apply Decay Process (88 minutes): Perform the calculation for the remaining mass after the first minute.\newlineRemaining mass after 11 minute = 230×0.723=166.29230 \times 0.723 = 166.29 grams
  5. Calculate Remaining Mass (88 minutes): Apply the decay process for 88 minutes.\newlineSince the decay happens each minute, we need to multiply the remaining mass by 0.7230.723 for each of the 88 minutes.\newlineRemaining mass after 88 minutes = 230×(0.723)8230 \times (0.723)^8
  6. Perform Calculation (88 minutes): Calculate the remaining mass after 88 minutes.\newlineRemaining mass after 88 minutes = 230×(0.723)8230 \times (0.723)^8
  7. Complete Calculation and Round: Perform the calculation for the remaining mass after 88 minutes.\newlineRemaining mass after 88 minutes = 230×(0.723)8≈230×0.100258230 \times (0.723)^8 \approx 230 \times 0.100258
  8. Complete Calculation and Round: Perform the calculation for the remaining mass after 88 minutes.\newlineRemaining mass after 88 minutes = 230×(0.723)8≈230×0.100258230 \times (0.723)^8 \approx 230 \times 0.100258Complete the calculation and round to the nearest 1010th of a gram.\newlineRemaining mass after 88 minutes ≈230×0.100258≈23.05934\approx 230 \times 0.100258 \approx 23.05934 grams\newlineRounded to the nearest 1010th of a gram, the remaining mass is approximately 23.123.1 grams.

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