Question An element with mass 210 grams decays by 8.3% per minute. How much of the element is remaining after 15 minutes, to the nearest 10th of a gram? Answer Attemptiout of 2

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Question An element with mass 210 grams decays by 8.3% per minute. How much of the element is remaining after 15 minutes, to the nearest 10th of a gram? Answer Attemptiout of 2

Answer 1

### 60.6 grams

Answer 2

## Step 1: Identify the decay formula ### The decay of an element can be modeled using the exponential decay formula: $M(t) = M_0 \cdot e^{kt}$, where $M(t)$ is the mass at time $t$, $M_0$ is the initial mass, $k$ is the decay constant, and $t$ is time. ## Step 2: Determine the decay constant ### The decay rate is given as 8.3% per minute, which means $k = -0.083$ per minute. This is because $k = \ln(\frac{M(t)}{M_0})/t$ and here $\ln(1 - 0.083) \approx -0.083$. ## Step 3: Apply the formula to find the remaining mass after 15 minutes ### Using the formula with $M_0 = 210$ grams, $k = -0.083$, and $t = 15$ minutes, we get: $$M(15) = 210 \cdot e^{-0.083 \cdot 15}$$ ## Step 4: Calculate the exponent ### Calculate the exponent value: $$-0.083 \cdot 15 = -1.245$$ ## Step 5: Compute the remaining mass ### Substitute the exponent back into the formula and compute: $$M(15) = 210 \cdot e^{-1.245} \approx 210 \cdot 0.2887 = 60.627 \text{ grams}$$ ## Step 6: Round the result ### Round to the nearest tenth of a gram: $60.6$ grams.

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Question An element with mass 210 grams decays by 8.3% per minute. How much of the element is remaining after 15 minutes, to the nearest 10th of a gram? Answer Attemptiout of 2

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