Question

an element with mass 420 grams decays by 11.8% per minute. how much of the element is remaining after 16 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, $P = 420$ grams, $r = 0.118$ (since 11.8% = 0.118), and $t = 16$ minutes.

Step2: Substitute the values into the formula

Substitute $P = 420$, $r = 0.118$, and $t = 16$ into the formula:
$A = 420(1 - 0.118)^{16}$

Step3: Calculate the value inside the parentheses

First, calculate $1 - 0.118 = 0.882$.

Step4: Calculate the exponent

Now, calculate $0.882^{16}$. Using a calculator, $0.882^{16}\approx0.1402$.

Step5: Multiply by the initial amount

Multiply this result by 420: $A = 420\times0.1402\approx58.9$.

Answer:

58.9