Question

an element with mass 210 grams decays by 8.3% per minute. how much of the element is remaining after 15 minutes, to the nearest 10th of a gram?

Explanation:

Step1: Identify the formula for exponential decay

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.

Step2: Convert the decay rate to decimal

The decay rate is 8.3%, so $r = \frac{8.3}{100} = 0.083$.

Step3: Substitute the values into the formula

We have $P = 210$, $r = 0.083$, and $t = 15$. So, $A = 210(1 - 0.083)^{15}$.

Step4: Calculate $(1 - 0.083)$

$1 - 0.083 = 0.917$.

Step5: Calculate $0.917^{15}$

Using a calculator, $0.917^{15} \approx 0.2903$.

Step6: Multiply by the initial amount

$A = 210 \times 0.2903 \approx 60.963$.

Step7: Round to the nearest tenth

Rounding 60.963 to the nearest tenth gives 61.0.

Answer:

61.0