question an element with mass 730 grams decays by 27.6% per minute. how much of the element is remaining…

question an element with mass 730 grams decays by 27.6% per minute. how much of the element is remaining after 12 minutes, to the nearest 10th of a gram?

question an element with mass 730 grams decays by 27.6% per minute. how much of the element is remaining after 12 minutes, to the nearest 10th of a gram?

Answer

Explanation:

Step1: Identify the 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, $A_0=730$ grams, $r = 0.276$, and $t = 12$ minutes.

Step2: Substitute the values into the formula

$A=730\times(1 - 0.276)^{12}$. First, calculate $1-0.276 = 0.724$. Then, find $(0.724)^{12}$. $(0.724)^{12}\approx0.00797$.

Step3: Calculate the remaining amount

$A = 730\times0.00797\approx5.8$ grams.

Answer:

$5.8$ grams