question\nan element with mass 590 grams decays by 19.5% per minute. how much of the element is remaining…

question\nan 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?

question\nan 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

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

[ \begin{align*} A&=590\times(1 - 0.195)^{15}\ &=590\times(0.805)^{15} \end{align*} ]

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

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

Step4: Calculate the final amount (A)

[ \begin{align*} A&=590\times0.0477\ &=28.143 \end{align*} ] Rounding to the nearest tenth, (A\approx28.1)

Answer:

(28.1) grams