Question

question
an element with mass 570 grams decays by 18% per minute. how much of the element is remaining after 13 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, $P = 570$ grams, $r = 0.18$ (since $18\% = 0.18$), and $t = 13$ minutes.

Step2: Substitute values into the formula

Substitute $P = 570$, $r = 0.18$, and $t = 13$ into the formula:
$A = 570(1 - 0.18)^{13}$
First, calculate $1 - 0.18 = 0.82$.
Then, calculate $0.82^{13}$. Let's compute that: $0.82^{13}\approx0.0752$ (using a calculator for the exponentiation).

Step3: Calculate the final amount

Now, multiply by the initial amount:
$A = 570\times0.0752$
$A\approx42.9$ (rounded to the nearest tenth of a gram)

Answer:

The remaining mass of the element is approximately $\boldsymbol{42.9}$ grams.