an element with mass 670 grams decays by 21.8% per minute. how much of the element is remaining after 15…

Explanation:

Step1: Identify the decay formula

The formula for exponential decay is $A = A_0(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $A_0=670$, $r = 0.218$, and $t = 15$.

Step2: Substitute the values into the formula

$A=670\times(1 - 0.218)^{15}$. First, calculate $1-0.218 = 0.782$. Then we have $A = 670\times(0.782)^{15}$.

Step3: Calculate $(0.782)^{15}$

Using a calculator, $(0.782)^{15}\approx0.0277$.

Step4: Calculate the remaining amount

$A=670\times0.0277 = 18.559$. Rounding to the nearest tenth, we get $A\approx18.6$.

Answer:

$18.6$