The half-life of a certain radioactive material is 78 hours. An initial amount of the material has a mass of 790 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 18 hours.
Round your answer to the nearest thousandth.
(1 point):
The exponential function that models the decay of the material is given by:
N(t) = N₀ * (1/2)^(t/h),
where N₀ is the initial amount of material (in this case, 790 kg), t is the time (in this case, 18 hours), and h is the half-life of the material (in this case, 78 hours).
Substituting the values into the equation, we have:
N(18) = 790 * (1/2)^(18/78)
Calculating this expression gives us:
N(18) ≈ 790 * 0.863
Rounding the result to the nearest thousandth gives us:
N(18) ≈ 681.770 kg
Therefore, after 18 hours, approximately 682 kg of radioactive material remains.