Question

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) Responses ; 0.107kg Image with alt text: y = 1/2(1/790)^1/78x ; 0.107kg y = 790; 0 kg y = 790 Image with alt text: one half to 78x ; 0 kg y = 2; 0.429 kg y = 2 Image with alt text: 1 over 790 to the 1 over 78x ; 0.429 kg y = 790; 673.233 kg

Answer 1

The correct exponential function that models the decay of the radioactive material is:

y = 790(1/2)^(1/78x)

To find how much radioactive material remains after 18 hours, plug in x = 18 into the equation:

y = 790(1/2)^(1/78 * 18)

y ≈ 673.233 kg

Therefore, about 673.233 kg of radioactive material remains after 18 hours.