Question

an element with mass 290 grams decays by 13.2% per minute. how much of the element is remaining after 14 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, $A$ = final mass.

Step2: Identify given values

$P = 290$, $r = 0.132$, $t = 14$

Step3: Calculate decay factor

$1 - r = 1 - 0.132 = 0.868$

Step4: Compute $(0.868)^{14}$

$(0.868)^{14} \approx 0.1472$

Step5: Find final mass

$A = 290 \times 0.1472$

Answer:

42.7 grams