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An element with mass 730 grams decays by 28.8% per minute. How much of the element is remaining after 10 minutes, to the nearest 10th of a gram?

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An element with mass 730 grams decays by 28.8% per minute. How much of the element is remaining after 10 minutes, to the nearest 10th of a gram?

An element with mass 730 grams decays by 28.8% per minute. How much of the element is remaining after 10 minutes, to the nearest 10th of a gram?

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TommyProfessional · Tutor for 6 years

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### 18.3 grams

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## Step 1: Identify the decay rate per minute<br />### The element decays by \( 28.8\% \) per minute, which means the remaining amount is \( 100\% - 28.8\% = 71.2\% \) per minute, or \( 0.712 \) times the previous amount.<br />## Step 2: Determine the decay formula<br />### The remaining mass \( m(t) \) after \( t \) minutes can be modelled by the formula \( m(t) = m_0 \times (decay\,factor)^t \), where \( m_0 \) is the initial mass and the decay factor is \( 0.712 \).<br />## Step 3: Calculate the remaining mass after 10 minutes<br />### Initial mass \( m_0 = 730 \) grams, decay factor = \( 0.712 \), and \( t = 10 \):<br />\[ m(10) = 730 \times 0.712^{10} \]<br />## Step 4: Compute the numerical value<br />### Using a calculator or computation tool:<br />\[ m(10) \approx 730 \times (0.02507) \approx 18.3 \]
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