Question

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?

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, $A_0=140$ grams, $r = 0.216$, and $t = 20$ minutes.

Step2: Substitute the values into the formula

$A=140\times(1 - 0.216)^{20}$.
First, calculate $1-0.216 = 0.784$. Then, find $(0.784)^{20}$. Using a calculator, $(0.784)^{20}\approx0.00197$.

Step3: Calculate the remaining amount

$A = 140\times0.00197\approx0.276$ grams. Rounding to the nearest tenth, $A\approx0.3$ grams.

Answer:

$0.3$ grams