Question

an element with mass 780 grams decays by 17.1% per minute. how much of the element is remaining after 19 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, $A$ = remaining mass.

Step2: Identify given values

$P = 780$ g, $r = 0.171$, $t = 19$ minutes

Step3: Substitute values into formula

$A = 780(1 - 0.171)^{19}$

Step4: Calculate the decay factor

$1 - 0.171 = 0.829$
$0.829^{19} \approx 0.02124$

Step5: Compute final remaining mass

$A = 780 \times 0.02124 \approx 16.5672$

Step6: Round to nearest tenth

Round $16.5672$ to 1 decimal place: $16.6$

Answer:

16.6 grams