an element with mass 570 grams decays by 26.9% per minute. how much of the element is remaining after 14…

Explanation:

Step1: Identify decay formula

The formula for exponential decay is $A = A_0(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $A_0=570$, $r = 0.269$, and $t = 14$.

Step2: Substitute values into formula

$A=570\times(1 - 0.269)^{14}=570\times0.731^{14}$.

Step3: Calculate $0.731^{14}$

Using a calculator, $0.731^{14}\approx0.01077$.

Step4: Calculate the remaining amount

$A = 570\times0.01077\approx6.1$.

Answer:

$6.1$ grams