an element with mass 310 grams decays by 8.9% per minute. how much of the element is remaining after 19…
an element with mass 310 grams decays by 8.9% per minute. how much of the element is remaining after 19 minutes, to the nearest 10th of a gram?
Answer
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.
Step2: Substitute values
Here, $A_0=310$ grams, $r = 0.089$, and $t = 19$. So, $A=310\times(1 - 0.089)^{19}$.
Step3: Calculate the value inside the parentheses
$1-0.089 = 0.911$.
Step4: Calculate the power
$(0.911)^{19}\approx0.1877$.
Step5: Calculate the final amount
$A = 310\times0.1877\approx58.2$.
Answer:
$58.2$ grams