Question

an element with mass 570 grams decays by 26.9% 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 $P$ = initial mass, $r$ = decay rate, $t$ = time, $A$ = remaining mass.

Step2: Identify given values

$P = 570$ g, $r = 0.269$, $t = 14$ minutes

Step3: Substitute values into formula

$A = 570(1 - 0.269)^{14}$

Step4: Calculate decay factor first

$1 - 0.269 = 0.731$
$0.731^{14} \approx 0.00602$

Step5: Compute final remaining mass

$A = 570 \times 0.00602 \approx 3.4314$

Step6: Round to nearest tenth

Round $3.4314$ to 1 decimal place.

Answer:

3.4 grams