Question

an element with mass 670 grams decays by 27.3% 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 $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay (in decimal), and $t$ is the time.
Here, $P = 670$ grams, $r = 0.273$ (since 27.3% = 0.273), and $t = 9$ minutes.

Step2: Substitute the values into the formula

Substitute $P = 670$, $r = 0.273$, and $t = 9$ into the formula:
$A = 670(1 - 0.273)^9$

Step3: Calculate the value inside the parentheses

First, calculate $1 - 0.273 = 0.727$.

Step4: Calculate the exponentiation

Now, calculate $0.727^9$. Using a calculator, $0.727^9 \approx 0.0602$.

Step5: Calculate the final amount

Multiply this result by 670: $A = 670 \times 0.0602 \approx 40.334$.

Step6: Round to the nearest tenth

Rounding 40.334 to the nearest tenth gives 40.3.

Answer:

40.3