Question

An element with mass 970 grams decay by 15.1% per minute. How much of the element is remaining after 14 minutes, to the nearest 10th of a gram?

Answer 1

The amount of the element remaining after 14 minutes can be found using the decay rate and half-life. After 14 minutes, approximately 660.4 grams of the element is remaining.

Step-by-step explanation:

To find out how much of the element is remaining after 14 minutes, we can use the formula:

Remaining mass = Initial mass × (1 - decay rate)^(time / half-life)

Given that the initial mass is 970 grams and the decay rate is 15.1% per minute, the half-life can be calculated using the formula:

half-life = (ln(1 - decay rate) / ln(2)) × 1 minute

Substituting the values into the formulas, we can find that:

half-life ≈ 4.57 minutes

Remaining mass ≈ 660.4 grams

Therefore, after 14 minutes, approximately 660.4 grams of the element is remaining.