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 $P$ = initial mass, $r$ = decay rate, $t$ = time.

Step2: Identify given values

$P = 640$ g, $r = 0.073$, $t = 8$ minutes.

Step3: Calculate remaining mass

Substitute values into the formula:
$A = 640(1 - 0.073)^8 = 640(0.927)^8$
First compute $0.927^8 \approx 0.5632$
Then $A \approx 640 \times 0.5632$

Answer:

360.4 grams