an element with mass 670 grams decays by 27.3% per minute. how much of the element is remaining after 9…

Answer:

$47.5$

Explanation:

Step1: Identify 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, $A_0=670$ grams, $r = 0.273$, and $t = 9$ minutes.

Step2: Substitute values into formula

$A=670\times(1 - 0.273)^9$. First, calculate $1 - r$: $1-0.273 = 0.727$. Then, calculate $(0.727)^9$. Using a calculator, $(0.727)^9\approx0.0709$.

Step3: Calculate the remaining amount

$A = 670\times0.0709$. $A=670\times0.0709 = 47.403$. Rounding to the nearest tenth of a gram, $A\approx47.5$ grams.