Question

an element with mass 590 grams decays by 19.5% per minute. how much of the element is remaining after 15 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

$P = 590$, $r = 0.195$, $t = 15$

Step3: Substitute values into formula

$A = 590(1 - 0.195)^{15}$

Step4: Calculate decay factor first

$1 - 0.195 = 0.805$
$0.805^{15} \approx 0.03507$

Step5: Compute final mass

$A \approx 590 \times 0.03507$

Answer:

$20.7$ grams