Q. 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:
Convert to Decimal: We need to calculate the remaining mass of the element after it decays by 6% per minute for 8 minutes. The decay process can be modeled by an exponential decay function.To find the remaining mass after each minute, we can use the formula:Remaining mass = Initial mass ×(1−decay rate)timewhere the decay rate is 6% or 0.06 as a decimal, and time is the number of minutes.
Apply Decay Rate: First, convert the decay rate percentage to a decimal by dividing by 100. Decay rate = 6%=1006=0.06
Calculate Remaining Mass: Now, apply the decay rate to the initial mass for 8 minutes using the formula.Remaining mass after 8 minutes = 650×(1−0.06)8
Find Decay Factor: Calculate the remaining mass.Remaining mass after 8 minutes = 650×(0.94)8
Multiply Initial Mass: Use a calculator to find (0.94)8.(0.94)8≈0.629856
Perform Multiplication: Multiply the initial mass by the decay factor to find the remaining mass.Remaining mass after 8 minutes ≈650×0.629856
Round Remaining Mass: Perform the multiplication to find the remaining mass.Remaining mass after 8 minutes ≈409.4064 grams
Round Remaining Mass: Perform the multiplication to find the remaining mass.Remaining mass after 8 minutes ≈409.4064 gramsRound the remaining mass to the nearest tenth of a gram.Remaining mass after 8 minutes ≈409.4 grams
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