Question

an element with mass 780 grams decays by 17.1% per minute. how much of the element is remaining after 19 minutes, to the nearest 10th of a gram?

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 as a decimal, and $t$ is the time. Here, $A_0=780$, $r = 0.171$, and $t = 19$.

Step2: Substitute the values into the formula

$A=780\times(1 - 0.171)^{19}=780\times0.829^{19}$.

Step3: Calculate $0.829^{19}$

Using a calculator, $0.829^{19}\approx0.0377$.

Step4: Calculate the final amount

$A = 780\times0.0377\approx29.4$.

Answer:

$29.4$