Question

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?

Explanation:

Step1: Identify the decay formula

The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time.
Here, $P = 310$ grams, $r = 8.9\% = 0.089$, and $t = 19$ minutes.

Step2: Substitute the values into the formula

Substitute $P = 310$, $r = 0.089$, and $t = 19$ into the formula:
$A = 310(1 - 0.089)^{19}$
First, calculate $1 - 0.089 = 0.911$.
Then, calculate $0.911^{19}$. Using a calculator, $0.911^{19}\approx0.1747$.
Now, multiply by 310: $A = 310\times0.1747\approx54.2$.

Answer:

The remaining mass of the element after 19 minutes is approximately $\boxed{54.2}$ grams.