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)
1/
1
178*
01=2\790)
0.107kg
01=780 178.
kg
1=21_1
78";
790,
0.429 kg
04=790178:
The exponential function that models the decay of this radioactive material is:
A(t) = A0 * (1/2)^(t/h)
where A(t) is the amount of radioactive material remaining at time t, A0 is the initial amount of radioactive material, t is the time elapsed, and h is the half-life of the material.
Plugging in the given values, we have:
A(t) = 790 * (1/2)^(t/78)
To find how much radioactive material remains after 18 hours, we substitute t = 18 into the equation:
A(18) = 790 * (1/2)^(18/78)
A(18) ≈ 790 * 0.509
A(18) ≈ 402.11
Rounded to the nearest thousandth, approximately 402.11 kg of radioactive material remains after 18 hours.