Question

question
an element with mass 390 grams decays by 19.5% per minute. how much of the element is remaining after 15 minutes, to the nearest tenth 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 per period, $t$ = time.

Step2: Identify given values

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

Step3: Calculate remaining mass

Substitute values into the formula:
$A = 590(1 - 0.195)^{15} = 590(0.805)^{15}$
First compute $0.805^{15} \approx 0.03627$
Then $A \approx 590 \times 0.03627 \approx 21.4$

Answer:

21.4 grams