Question

an element with mass 730 grams decays by 28.8% per minute. how much of the element is remaining after 10 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, $A_0=730$ grams, $r = 0.288$, and $t = 10$.

Step2: Substitute the values into the formula

$A=730\times(1 - 0.288)^{10}$.
First, calculate $1-0.288 = 0.712$. Then we have $A = 730\times(0.712)^{10}$.

Step3: Calculate $(0.712)^{10}$

$(0.712)^{10}\approx0.02827$.

Step4: Calculate the final amount

$A = 730\times0.02827\approx20.6$ grams.

Answer:

$20.6$ grams