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?

Explanation:

Step1: Define decay formula

The exponential decay formula is $A = P(1 - r)^t$, where $P$ is initial mass, $r$ is decay rate, $t$ is time.

Step2: Identify given values

$P = 730$, $r = 0.276$, $t = 12$

Step3: Calculate decay factor

$1 - r = 1 - 0.276 = 0.724$

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

$(0.724)^{12} \approx 0.01915$

Step5: Find remaining mass

$A = 730 \times 0.01915$

Answer:

13.9 grams