An element with mass 490 grams decays by 18.8% 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 490 grams decays by  18.8% 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 the problem: Understand the problem. We need to calculate the remaining mass of an element after it decays by 18.8% per minute for 8 minutes. Initial mass of the element: 490 grams Decay rate per minute: 18.8% Time of decay: 8 minutes We will use the formula for exponential decay to find the remaining mass.Calculate decay factor: Calculate the decay factor per minute. The decay factor is the percentage of the substance that remains after each minute. Since the element decays by 18.8%, the remaining percentage each minute is 100% - 18.8% = 81.2%. To use this in calculations, we convert the percentage to a decimal by dividing by 100. Decay factor per minute = 81.2 / 100 = 0.812Apply exponential decay formula: Apply the exponential decay formula. The formula for the remaining mass after a certain number of minutes is: Remaining mass = Initial mass * (Decay factor)^number of minutes Let's plug in the values: Remaining mass after 8 minutes = 490 * (0.812)^8Calculate remaining mass: Calculate the remaining mass after 8 minutes. Now we need to calculate 0.812 raised to the power of 8 and then multiply it by 490 grams. Remaining mass after 8 minutes = 490 * (0.812)^8 Using a calculator, (0.812)^8 ≈ 0.1693 (rounded to four decimal places) Remaining mass after 8 minutes ≈ 490 * 0.1693 Remaining mass after 8 minutes ≈ 82.9557 gramsRound the result: Round the result to the nearest 10th of a gram. We round 82.9557 grams to the nearest 10th, which gives us 83.0 grams.

An element with mass $490$ grams decays by $18.8 \%$ 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 $490$ grams decays by $18.8 \%$ per minute. How much of the element is remaining after $8$ minutes, to the nearest $1$ oth of a gram? $\newline$ Answer: