an element with mass 820 grams decays by 26.8% per minute. how much of the element is remaining after 18…

Explanation:

Step1: Identify 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=820), (r = 0.268), and (t = 18).

Step2: Substitute the values into the formula

[ \begin{align*} A&=820\times(1 - 0.268)^{18}\ &=820\times(0.732)^{18} \end{align*} ]

Step3: Calculate ((0.732)^{18})

Using a calculator, ((0.732)^{18}\approx0.00373)

Step4: Calculate the remaining amount

[ \begin{align*} A&=820\times0.00373\ &=3.0586\approx3.1 \end{align*} ]

Answer:

(3.1) grams