question\nan element with mass 780 grams decays by 16.3% per minute. how much of the element is remaining…

question\nan element with mass 780 grams decays by 16.3% per minute. how much of the element is remaining after 16 minutes, to the nearest 10th of a gram?

question\nan element with mass 780 grams decays by 16.3% per minute. how much of the element is remaining after 16 minutes, to the nearest 10th of a gram?

Answer

Explanation:

Step1: Define decay formula

The exponential decay formula is $A = P(1 - r)^t$, where:

  • $P = 780$ (initial mass),
  • $r = 0.163$ (decay rate per minute),
  • $t = 16$ (time in minutes).

Step2: Calculate remaining factor

First find the remaining fraction per minute: $1 - 0.163 = 0.837$. Then calculate $0.837^{16}$: $0.837^{16} \approx 0.0498$

Step3: Compute final mass

Multiply initial mass by the factor: $A = 780 \times 0.837^{16} \approx 780 \times 0.0498$

Answer:

38.8 grams