an element with mass 970 grams decays by 27.7% per minute. how much of the element is remaining after 13…

Explanation:

Step1: Determine 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 = 970), (r=0.277), and (t = 13).

Step2: Substitute the values into the formula

[ \begin{align*} A&=970\times(1 - 0.277)^{13}\ &=970\times(0.723)^{13} \end{align*} ]

Step3: Calculate ((0.723)^{13})

Using a calculator, ((0.723)^{13}\approx0.00719)

Step4: Calculate the final amount (A)

[ \begin{align*} A&=970\times0.00719\ &=6.9743\approx7.0 \end{align*} ]

Answer:

(7.0)