an element with mass 490 grams decays by 28.6% per minute. how much of the element is remaining after 16…

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 as a decimal, and $t$ is the time. Here, $A_0=490$, $r = 0.286$, and $t = 16$.

Step2: Substitute the values into the formula

$A=490\times(1 - 0.286)^{16}=490\times0.714^{16}$.

Step3: Calculate $0.714^{16}$

Using a calculator, $0.714^{16}\approx0.00377$.

Step4: Calculate the remaining amount

$A = 490\times0.00377\approx1.8$.

Answer:

$1.8$ grams