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 per period, $t$ = time, $A$ = remaining mass.

Step2: Identify given values

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

Step3: Substitute values into formula

$A = 730(1 - 0.276)^{12}$

Step4: Calculate the decay factor

First compute $1 - 0.276 = 0.724$, then $0.724^{12} \approx 0.01702$

Step5: Compute final remaining mass

$A = 730 \times 0.01702 \approx 12.4246$

Step6: Round to nearest tenth

Round $12.4246$ to 1 decimal place.

Answer:

12.4 grams