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 remaining mass

Substitute values: $A = 970(1 - 0.277)^{13} = 970(0.723)^{13}$
First compute $0.723^{13} \approx 0.01302$, then $970 \times 0.01302 \approx 12.6$

Answer:

12.6 grams