Question

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?

Explanation:

Step1: Identify the decay formula

The formula for exponential decay is \(A = P(1 - r)^t\), where \(P\) is the initial amount, \(r\) is the rate of decay, and \(t\) is the time.
Here, \(P = 590\), \(r=0.195\), and \(t = 15\).

Step2: Substitute the values into the formula

$$
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$$

Step3: Calculate \((0.805)^{15}\)

Using a calculator, \((0.805)^{15}\approx0.0477\)

Step4: Calculate the final amount \(A\)

$$
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$$

Rounding to the nearest tenth, \(A\approx28.1\)

Answer:

\(28.1\) grams