question\nan element with mass 570 grams decays by 18% per minute. how much of the element is remaining…

question\nan element with mass 570 grams decays by 18% per minute. how much of the element is remaining after 13 minutes, to the nearest 10th of a gram?

question\nan element with mass 570 grams decays by 18% per minute. how much of the element is remaining after 13 minutes, to the nearest 10th of a gram?

Answer

Explanation:

Step1: Identify the decay formula

The formula for exponential decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $P = 570$ grams, $r=0.18$, and $t = 13$.

Step2: Substitute the values into the formula

$A=570\times(1 - 0.18)^{13}=570\times0.82^{13}$.

Step3: Calculate $0.82^{13}$

$0.82^{13}\approx0.0897$.

Step4: Calculate the remaining amount $A$

$A = 570\times0.0897\approx51.1$.

Answer:

$51.1$ grams