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

$A = 310(1 - 0.089)^{19} = 310(0.911)^{19}$

Step4: Calculate $(0.911)^{19}$

$(0.911)^{19} \approx 0.1822$

Step5: Compute final mass

$A \approx 310 \times 0.1822$

Answer:

56.5 grams