Question

consider the following scenario. a sample of radioactive material has a decay constant of 0.04 per hour. if there are initially 500 grams of the material, how much will remain after 3 hours? (5 points)$y = 500(0.96)^3$$y = 3(0.96)^{500}$$y = 3(0.04)^{500}$$y = 500(0.04)^3$

Explanation:

Step1: Recall radioactive decay formula

The general formula for exponential decay is $y = N_0(1 - r)^t$, where $N_0$ is initial amount, $r$ is decay rate, $t$ is time.

Step2: Identify given values

$N_0 = 500$, $r = 0.04$, $t = 3$

Step3: Calculate decay factor

$1 - r = 1 - 0.04 = 0.96$

Step4: Substitute into formula

$y = 500(0.96)^3$

Answer:

$y = 500(0.96)^3$