an element with mass 420 grams decays by 11.8% per minute. how much of the element is remaining after 16…

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, $A_0=420$, $r = 0.118$, and $t = 16$.

Step2: Substitute the values into the formula

$A=420\times(1 - 0.118)^{16}$. First, calculate $1-0.118 = 0.882$. Then we have $A = 420\times(0.882)^{16}$.

Step3: Calculate $(0.882)^{16}$

Using a calculator, $(0.882)^{16}\approx0.1477$.

Step4: Calculate the remaining amount

$A = 420\times0.1477=62.034$. Rounding to the nearest tenth, $A\approx62.0$.

Answer:

$62.0$ grams