An element with mass 570 grams decays by 15.2% per minute. How much of the element is remaining after 16 minutes, to the nearest 1oth of a gram? Answer:

Question

An element with mass 570 grams decays by  15.2% per minute. How much of the element is remaining after 16 minutes, to the nearest 1oth of a gram? Answer:

Bytelearn · Accepted Answer

Understand the problem: Understand the problem and determine the formula to use. We know that the element decays by 15.2% per minute. This means that each minute, the element retains 100% - 15.2% = 84.8% of its mass from the previous minute. To find the remaining mass after 16 minutes, we will apply the decay percentage repeatedly for 16 times.Convert to decimal: Convert the decay percentage to a decimal to use in calculations. 15.2% as a decimal is 15.2 / 100 = 0.152. Therefore, the remaining percentage as a decimal is 1 - 0.152 = 0.848.Calculate remaining mass: Calculate the remaining mass after each minute. We will use the formula for exponential decay, which is: Remaining mass = Initial mass * (1 - decay rate) ^ number of time periods In this case, the initial mass is 570 grams, the decay rate is 0.152, and the number of time periods is 16 minutes.Perform calculation: Perform the calculation using the formula. Remaining mass after 16 minutes = 570 * (0.848) ^ 16Calculate exact value: Calculate the exact value using a calculator. Remaining mass after 16 minutes ≈ 570 * (0.848) ^ 16 ≈ 570 * 0.049 ≈ 27.93 gramsRound the result: Round the result to the nearest tenth of a gram. The remaining mass after 16 minutes, rounded to the nearest tenth of a gram, is approximately 27.9 grams.

An element with mass $570$ grams decays by $15.2 \%$ per minute. How much of the element is remaining after $16$ minutes, to the nearest $1$ oth of a gram? $\newline$ Answer:

Full solution

More problems from Percent error

Related topics

An element with mass 570570570 grams decays by 15.2% 15.2 \% 15.2% per minute. How much of the element is remaining after 161616 minutes, to the nearest 111oth of a gram?\newlineAnswer:

An element with mass $570$ grams decays by $15.2 \%$ per minute. How much of the element is remaining after $16$ minutes, to the nearest $1$ oth of a gram? $\newline$ Answer: