Question

an element with mass 670 grams decays by 21.8% per minute. how much of the element is remaining after 15 minutes, to the nearest 10th of a gram?

Explanation:

Step1: Identify the decay formula

The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time.

Step2: Convert the decay rate to a decimal

The decay rate is $21.8\%$, so $r = 0.218$.

Step3: Substitute the values into the formula

We have $P = 670$, $r = 0.218$, and $t = 15$. So the formula becomes $A = 670(1 - 0.218)^{15}$.

Step4: Calculate $(1 - 0.218)$

$1 - 0.218 = 0.782$.

Step5: Calculate $0.782^{15}$

Using a calculator, $0.782^{15} \approx 0.0342$.

Step6: Calculate $A$

$A = 670 \times 0.0342 \approx 22.914$.

Step7: Round to the nearest tenth

Rounding $22.914$ to the nearest tenth gives $22.9$.

Answer:

The remaining mass of the element after 15 minutes is approximately $\boxed{22.9}$ grams.