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

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

Step3: Calculate remaining mass

Substitute values: $A = 290(1 - 0.132)^{14} = 290(0.868)^{14}$
First compute $0.868^{14} \approx 0.1477$, then $290 \times 0.1477 \approx 42.833$

Step4: Round to nearest tenth

Round $42.833$ to one decimal place.

Answer:

42.8 grams