an element with mass 290 grams decays by 13.2% 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, $A_0=290$ grams, $r = 0.132$, and $t = 14$ minutes.

Step2: Substitute values into formula

$A=290\times(1 - 0.132)^{14}=290\times(0.868)^{14}$.

Step3: Calculate $(0.868)^{14}$

Using a calculator, $(0.868)^{14}\approx0.1497$.

Step4: Calculate the final amount

$A = 290\times0.1497\approx43.4$ grams.

Answer:

$43.4$ grams