Question

an element with mass 970 grams decays by 15.1% per minute. how much of the element is remaining after 10 minutes?

Explanation:

Step1: Determine the decay - factor

The element decays by 15.1% per minute. So the remaining fraction per minute is $1 - 0.151=0.849$.

Step2: Set up the decay formula

The formula for exponential decay is $A = A_0\times(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $A_0 = 970$ grams, $r = 0.151$, and $t = 14$ minutes.

Step3: Calculate the remaining amount

Substitute the values into the formula: $A=970\times(0.849)^{14}$.
First, calculate $(0.849)^{14}$. Using a calculator, $(0.849)^{14}\approx0.1004$.
Then, $A = 970\times0.1004\approx97.4$ grams.

Answer:

Approximately 97.4 grams