The half-life of a certain radioactive material is 42 days. An initial amount of the material has a mass of 49 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 8 days. Round your answer to the nearest thousandth.
To model the decay of the radioactive material, we can use the exponential decay formula:
A(t) = A0 * (1/2)^(t/h)
where:
A(t) = amount of material remaining after time t
A0 = initial amount of material
t = time elapsed
h = half-life
Plugging in the given values:
A(t) = 49 * (1/2)^(t/42)
To find how much material remains after 8 days:
A(8) = 49 * (1/2)^(8/42)
A(8) = 49 * (1/2)^(0.190476)
A(8) = 49 * 0.751315
A(8) = 36.794
Rounded to the nearest thousandth, 36.794 kg of radioactive material remains after 8 days.