Question

question
an element with mass 310 grams decays by 5.7% per minute. how much of the element is remaining after 9 minutes, to the nearest 10th of a gram?

Explanation:

Step1: Define decay formula

The exponential decay formula is $A = P(1 - r)^t$, where $P=310$ (initial mass), $r=0.057$ (decay rate), $t=9$ (time in minutes).

Step2: Substitute values into formula

$A = 310(1 - 0.057)^9$

Step3: Calculate decay factor first

$1 - 0.057 = 0.943$
$0.943^9 \approx 0.6172$

Step4: Compute final mass

$A \approx 310 \times 0.6172$

Answer:

191.3 grams