Question

an element with mass 640 grams decays by 7.3% per minute. how much of the element is remaining after 8 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

$P = 640$, $r = 0.073$, $t = 8$

Step3: Calculate remaining mass

Substitute values: $A = 640(1 - 0.073)^8 = 640(0.927)^8$
First compute $0.927^8 \approx 0.5737$, then $640 \times 0.5737 \approx 367.168$

Step4: Round to nearest tenth

Round $367.168$ to one decimal place.

Answer:

367.2 grams