Question

an element with mass 730 grams decays by 27.6% per minute. how much of the element is remaining after 12 minutes, to the nearest 10th of a gram? answer attempt 1 out of 2

Explanation:

Step1: Identify 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 (in decimal), and $t$ is time.

Step2: Convert decay rate to decimal

Given $r = 27.6\% = 0.276$.

Step3: Substitute values into formula

$P = 730$, $r = 0.276$, $t = 12$. So $A = 730(1 - 0.276)^{12} = 730(0.724)^{12}$.

Step4: Calculate $(0.724)^{12}$

First, compute $0.724^{12}$. Using a calculator, $0.724^{12} \approx 0.0173$.

Step5: Multiply by initial amount

$A = 730 \times 0.0173 \approx 12.6$.

Answer:

12.6