Question

an element with mass 290 grams decays by 13.2% per minute. how much of the element is remaining after 14 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

$P = 290$ grams, $r = 0.132$, $t = 14$ minutes

Step3: Substitute values into formula

$A = 290(1 - 0.132)^{14}$

Step4: Calculate decay factor first

$1 - 0.132 = 0.868$; $0.868^{14} \approx 0.1472$

Step5: Compute final remaining mass

$A \approx 290 \times 0.1472$

Answer:

42.7 grams