An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest 10 th of a gram?

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Identify values: Identify the initial amount, decay rate per minute, and total time. Initial amount (a) = 780 grams Decay rate per minute (r) = 16.3% Total time (t) = 16 minutesConvert to decimal: Convert the decay rate from a percentage to a decimal. To convert a percentage to a decimal, divide by 100. r = 16.3% / 100 = 0.163Determine decay factor: Determine the decay factor per minute. The decay factor is the amount by which the substance decreases each minute. Since it decays by 16.3%, it retains 100% - 16.3% = 83.7% of its mass each minute. Decay factor per minute = 1 - r = 1 - 0.163 = 0.837Calculate remaining amount: Calculate the remaining amount of the element after 16 minutes. The formula for exponential decay is: remaining amount = initial amount * (decay factor)^(total time) Substitute the known values into the formula: remaining amount = 780 * (0.837)^16Perform calculation: Perform the calculation. Use a calculator to compute the remaining amount: remaining amount = 780 * (0.837)^16 remaining amount ≈ 780 * 0.0494 (rounded to 4 decimal places) remaining amount ≈ 38.532 (rounded to 3 decimal places)Round to nearest tenth: Round the result to the nearest tenth of a gram. To round to the nearest tenth, look at the hundredths place. If it is 5 or more, round up; if it is less than 5, round down. remaining amount ≈ 38.5 grams (since the hundredths place is 3, we round down)

An element with mass $780$ grams decays by $16.3 \%$ per minute. How much of the element is remaining after $16$ minutes, to the nearest $10$ th of a gram?

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An element with mass $780$ grams decays by $16.3 \%$ per minute. How much of the element is remaining after $16$ minutes, to the nearest $10$ th of a gram?