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 $P$ = initial mass, $r$ = decay rate, $t$ = time.

Step2: Identify given values

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

Step3: Calculate remaining mass

Substitute values: $A = 730(1 - 0.276)^{12} = 730(0.724)^{12}$
First compute $0.724^{12} \approx 0.0191$
Then $A \approx 730 \times 0.0191 \approx 13.943$

Step4: Round to nearest tenth

Round $13.943$ to 1 decimal place.

Answer:

13.9 grams