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 (in decimal), and \( t \) is the time.
Here, \( P = 420 \) grams, \( r = 11.8\% = 0.118 \), and \( t = 16 \) minutes.

Step2: Substitute values into the formula

Substitute \( P = 420 \), \( r = 0.118 \), and \( t = 16 \) into \( A = P(1 - r)^t \):
\( A = 420(1 - 0.118)^{16} \)
First, calculate \( 1 - 0.118 = 0.882 \).
Then, calculate \( 0.882^{16} \). Using a calculator, \( 0.882^{16} \approx 0.1447 \).
Now, multiply by 420: \( A = 420 \times 0.1447 \approx 60.8 \)

Answer:

\( 60.8 \) grams