Question

an element with mass 210 grams decays by 8.3% 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:

• $P = 210$ (initial mass),
• $r = 0.083$ (decay rate per minute),
• $t = 15$ (time in minutes).

Step2: Substitute values into formula

$A = 210(1 - 0.083)^{15}$

Step3: Calculate decay factor first

$1 - 0.083 = 0.917$
$0.917^{15} \approx 0.2825$

Step4: Compute final mass

$A = 210 \times 0.2825 \approx 59.325$

Step5: Round to nearest tenth

Round $59.325$ to one decimal place.

Answer:

59.3 grams