Question

An element with mass 590 grams decays by 19.5% per minute. How much of the element is remaining after 15 minutes, to the nearest 10th of a gram?

Answer 1

To find the remaining amount of an element after 15 minutes decaying by 19.5% per minute, use the exponential decay formula. After calculations, approximately 22.7 grams of the element remain after 15 minutes, to the nearest tenth of a gram.

Step-by-step explanation:

An element that decays by a certain percentage per minute can be modeled using exponential decay. In this case, the element decays by 19.5% each minute. The amount of element remaining after t minutes can be calculated using the formula:

remaining amount = initial amount × (1 - decay rate)t

Let's calculate the remaining amount of the element after 15 minutes:

1. Initial amount = 590 grams
2. Decay rate per minute = 19.5% or 0.195 when expressed as a decimal
3. Time (t) = 15 minutes
4. Calculate the remaining amount using the formula:

remaining amount = 590 × (1 - 0.195)15

Using a calculator, we find the remaining amount after 15 minutes to be approximately 22.7 grams, rounded to the nearest tenth of a gram.