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 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 (as a decimal), and $t$ is the time.
Here, $P = 210$ grams, $r = 0.083$ (since 8.3% = 0.083), and $t = 15$ minutes.

Step2: Substitute the values into the formula

Substitute $P = 210$, $r = 0.083$, and $t = 15$ into the formula:
$A = 210(1 - 0.083)^{15}$
First, calculate $1 - 0.083 = 0.917$.
Then, calculate $0.917^{15}$. Using a calculator, $0.917^{15}\approx0.2603$.

Step3: Calculate the final amount

Multiply 210 by 0.2603:
$A = 210\times0.2603\approx54.7$

Answer:

54.7