Question

an element with mass 970 grams decays by 15.1% per minute. how much of the element is remaining after 14 minutes, to the nearest 10th of a gram? answer attempt 2 out of 2 submit answer

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, \(A_0=970\), \(r = 0.151\), and \(t = 14\).

Step2: Substitute the values into the formula

Substitute the values into the formula: \(A=970\times(1 - 0.151)^{14}\). First, calculate \(1-0.151=0.849\). Then we have \(A = 970\times(0.849)^{14}\).

Step3: Calculate \((0.849)^{14}\)

Using a calculator, \((0.849)^{14}\approx0.109\).

Step4: Calculate the final amount \(A\)

Multiply \(970\) by \(0.109\): \(A=970\times0.109 = 105.73\approx105.7\)

Answer:

\(105.7\)