Question

an element with mass 290 grams decays by 13.2% per minute. how much of the element is remaining after 14 minutes, to the nearest 10th of a gram?

Explanation:

Step1: Determine the decay formula

The formula for exponential decay is \(A = A_0(1 - r)^t\), where \(A_0\) is the initial amount, \(r\) is the rate of decay, and \(t\) is the time. Here, \(A_0=290\), \(r = 0.132\), and \(t = 14\).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step3: Calculate \((0.868)^{14}\)

Using a calculator, \((0.868)^{14}\approx0.1447\)

Step4: Calculate the final amount \(A\)

$$
LATEXBLOCK1
$$

Rounding to the nearest tenth, \(A\approx42.0\)

Answer:

\(42.0\) grams