question an element with mass 140 grams decay...
question an element with mass 140 grams decays by 21.6% per minute. how much of the element is remaining after 20 minutes, to the nearest 10th of a gram?
Answer
# Answer:
0.1
# 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, $A_0=140$, $r = 0.216$, and $t = 20$.
## Step2: Substitute values into formula
$A=140\times(1 - 0.216)^{20}=140\times0.784^{20}$.
## Step3: Calculate $0.784^{20}$
Using a calculator, $0.784^{20}\approx0.000714$.
## Step4: Calculate the remaining amount
$A = 140\times0.000714\approx0.1$.