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An element with mass 990 grams decays by
18.8% per minute. How much of the element is remaining after 13 minutes, to the nearest 1oth of a gram?
Answer:

An element with mass $990$ grams decays by $18.8 \%$ per minute. How much of the element is remaining after $13$ minutes, to the nearest $1$ oth of a gram? $\newline$ Answer:

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Full solution

Q. An element with mass

990

grams decays by

18.8 \%

per minute. How much of the element is remaining after

13

minutes, to the nearest

1

oth of a gram?

\newline

Answer:

Understand Problem: Understand the problem and determine what is being asked. $\newline$ We need to calculate the remaining mass of an element after it decays by $18.8\%$ per minute for $13$ minutes.
Calculate Decay Factor: Calculate the decay factor per minute. The decay factor is the percentage that remains after the decay occurs. Since the element decays by $18.8\%$ , the remaining percentage 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 = $81.2\% / 100 = 0.812$
Apply Decay Factor: Apply the decay factor for $13$ minutes. $\newline$ To find the remaining mass after $13$ minutes, we multiply the initial mass by the decay factor raised to the power of the number of minutes. $\newline$ Remaining mass after $13$ minutes = Initial mass $\times$ (Decay factor) $^{13}$
Perform Calculation: Perform the calculation using the initial mass and the decay factor. $\newline$ Initial mass = $990$ grams $\newline$ Remaining mass after $13$ minutes = $990 \times (0.812)^{13}$
Calculate Remaining Mass: Calculate the remaining mass using a calculator. $\newline$ Remaining mass after $13$ minutes $\approx 990 \times (0.812)^{13} \approx 990 \times 0.105 \approx 103.95$ grams
Round Result: Round the result to the nearest tenth of a gram. $\newline$ The remaining mass after $13$ minutes, rounded to the nearest tenth of a gram, is approximately $104.0$ grams.

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