Question

an element with mass 310 grams decays by 8.9% 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.

Step2: Identify given values

$P = 310$, $r = 0.089$, $t = 19$

Step3: Substitute values into formula

$A = 310(1 - 0.089)^{19}$

Step4: Calculate the decay factor

$1 - 0.089 = 0.911$; $0.911^{19} \approx 0.1702$

Step5: Compute final mass

$A = 310 \times 0.1702 \approx 52.762$

Step6: Round to nearest tenth

Round 52.762 to 52.8

Answer:

52.8 grams