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An element with mass 650 grams decays by 
6% per minute. How much of the element is remaining after 8 minutes, to the nearest 1oth of a gram?
Answer:

An element with mass 650650 grams decays by 6% 6 \% per minute. How much of the element is remaining after 88 minutes, to the nearest 11oth of a gram?\newlineAnswer:

Full solution

Q. An element with mass 650650 grams decays by 6% 6 \% per minute. How much of the element is remaining after 88 minutes, to the nearest 11oth of a gram?\newlineAnswer:
  1. Convert to Decimal: We need to calculate the remaining mass of the element after it decays by 6%6\% per minute for 88 minutes. The decay process can be modeled by an exponential decay function.\newlineTo find the remaining mass after each minute, we can use the formula:\newlineRemaining mass == Initial mass ×(1decay rate)time\times (1 - \text{decay rate})^{\text{time}}\newlinewhere the decay rate is 6%6\% or 0.060.06 as a decimal, and time is the number of minutes.
  2. Apply Decay Rate: First, convert the decay rate percentage to a decimal by dividing by 100100. Decay rate = 6%=6100=0.066\% = \frac{6}{100} = 0.06
  3. Calculate Remaining Mass: Now, apply the decay rate to the initial mass for 88 minutes using the formula.\newlineRemaining mass after 88 minutes = 650×(10.06)8650 \times (1 - 0.06)^8
  4. Find Decay Factor: Calculate the remaining mass.\newlineRemaining mass after 88 minutes = 650×(0.94)8650 \times (0.94)^8
  5. Multiply Initial Mass: Use a calculator to find (0.94)8(0.94)^8.(0.94)80.629856(0.94)^8 \approx 0.629856
  6. Perform Multiplication: Multiply the initial mass by the decay factor to find the remaining mass.\newlineRemaining mass after 88 minutes 650×0.629856\approx 650 \times 0.629856
  7. Round Remaining Mass: Perform the multiplication to find the remaining mass.\newlineRemaining mass after 88 minutes 409.4064\approx 409.4064 grams
  8. Round Remaining Mass: Perform the multiplication to find the remaining mass.\newlineRemaining mass after 88 minutes 409.4064\approx 409.4064 gramsRound the remaining mass to the nearest tenth of a gram.\newlineRemaining mass after 88 minutes 409.4\approx 409.4 grams

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