an element with mass 590 grams decays by 19.5% per minute. how much of the element is remaining after 15…

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 as a decimal, and $t$ is the time. Here, $P = 590$, $r=0.195$, and $t = 15$.

Step2: Substitute the values into the formula

$A=590\times(1 - 0.195)^{15}$. First, calculate $1-0.195 = 0.805$. Then we have $A = 590\times(0.805)^{15}$.

Step3: Calculate $(0.805)^{15}$

Using a calculator, $(0.805)^{15}\approx0.03977$.

Step4: Calculate the remaining amount $A$

$A = 590\times0.03977\approx23.5$.

Answer:

$23.5$ grams