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? Write and equation for this scenario.

Answer 1

The equation for radioactive decay is given by the formula:

N(t) = N₀ * e^(-kt)

Where:
N(t) = the amount of material remaining after time t
N₀ = the original amount of material
k = decay constant
t = time

In this scenario:
N₀ = 500 grams
k = 0.04 per hour
t = 3 hours

Plugging in the values:
N(3) = 500 * e^(-0.04*3)

N(3) = 500 * e^(-0.12)

Now, calculate the value of N(3):
N(3) = 500 * e^(-0.12)
N(3) ≈ 500 * 0.888
N(3) ≈ 444 grams

Therefore, after 3 hours, approximately 444 grams of the radioactive material will remain.