Question

an element with mass 970 grams decays by 27.7% per minute. how much of the element is remaining after 13 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

$P=970$, $r=0.277$, $t=13$

Step3: Calculate decay factor

$1-r = 1-0.277 = 0.723$

Step4: Compute $(0.723)^{13}$

$(0.723)^{13} \approx 0.01302$

Step5: Find remaining mass

$A = 970 \times 0.01302 \approx 12.6$

Answer:

12.6 grams