an element with mass 570 grams decays by 18% per minute. how much of the element is remaining after 13…

Explanation:

Step1: Identify the decay - formula

The formula for exponential decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $P = 570$ grams, $r=0.18$, and $t = 13$ minutes.

Step2: Substitute the values into the formula

$A=570\times(1 - 0.18)^{13}$. First, calculate $1-0.18 = 0.82$. Then we have $A = 570\times(0.82)^{13}$.

Step3: Calculate $(0.82)^{13}$

Using a calculator, $(0.82)^{13}\approx0.0937$.

Step4: Calculate the remaining amount $A$

$A = 570\times0.0937=53.309\approx53.3$ grams.

Answer:

$53.3$ grams