An element with mass 910 grams decays by 16.6% per minute. How much of the element is remaining after 20 minutes, to the nearest 1oth of a gram? Answer:

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An element with mass 910 grams decays by  16.6% per minute. How much of the element is remaining after 20 minutes, to the nearest 1oth of a gram? Answer:

Bytelearn · Accepted Answer

Understand Problem and Formula: Understand the problem and determine the formula to use. We know that the element decays by 16.6% per minute. This means that each minute, the element retains 100% - 16.6% = 83.4% of its mass from the previous minute. To find the remaining mass after 20 minutes, we can use the formula for exponential decay: Remaining mass = Initial mass * (1 - decay rate) ^ time where the decay rate is 16.6% or 0.166, and time is 20 minutes.Convert Decay Rate: Convert the decay rate to a decimal and calculate the remaining percentage each minute. Decay rate as a decimal = 16.6% / 100 = 0.166 Remaining percentage each minute = 1 - 0.166 = 0.834Apply Exponential Decay: Apply the exponential decay formula to calculate the remaining mass after 20 minutes. Remaining mass = 910 grams * (0.834) ^ 20Calculate Remaining Mass: Calculate the remaining mass using the values from the previous step. Remaining mass = 910 * (0.834) ^ 20Perform Calculation: Perform the calculation. Remaining mass ≈ 910 * (0.834) ^ 20 ≈ 910 * 0.049 ≈ 44.59 gramsRound Remaining Mass: Round the remaining mass to the nearest 10th of a gram. Rounded remaining mass = 44.6 grams

An element with mass $910$ grams decays by $16.6 \%$ per minute. How much of the element is remaining after $20$ minutes, to the nearest $1$ oth of a gram? $\newline$ Answer:

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An element with mass $910$ grams decays by $16.6 \%$ per minute. How much of the element is remaining after $20$ minutes, to the nearest $1$ oth of a gram? $\newline$ Answer: