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
y = 1/2(1/790)^1/78x; 0.107kg
Image with alt text: y = 1/2(1/790)^1/78x ; 0.107kg
y = 790one half to 78x; 0 kg
y = 790 Image with alt text: one half to 78x ; 0 kg
y = 21 over 790 to the 1 over 78x; 0.429 kg
y = 2 Image with alt text: 1 over 790 to the 1 over 78x ; 0.429 kg
y = 790one half to the 1 over 78x; 673.233 kg
The correct exponential function is: y = 790 * (1/2)^(x/78)
After 18 hours, the amount of radioactive material remaining is: y = 790 * (1/2)^(18/78) = 673.233 kg
Therefore, after 18 hours, approximately 673.233 kg of radioactive material remains.