Question

an element with mass 310 grams decays by 5.7% per minute. how much of the element is remaining after 9 minutes, to the nearest 10th of a gram?

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, $A_0=310$ grams, $r = 0.057$, and $t = 9$.

Step2: Substitute the values into the formula

$A=310\times(1 - 0.057)^9$. First, calculate $1-0.057 = 0.943$. Then, find $(0.943)^9$. Using a calculator, $(0.943)^9\approx0.5927$.

Step3: Calculate the remaining amount

Multiply the initial amount by the result of the exponentiation: $A = 310\times0.5927\approx183.7$.

Answer:

$183.7$ grams