The half-life of a certain radioactive material is 38 days. An initial amount of the material has a mass of 497 kg. Write an exp
onential function that models the decay of this material. Find how much radioactive material remains after 4 days. Round your answer to the nearest thousandth. (1 point) A ; 462.029 kg B ; 0.087 kg C ; 1.040 kg D ; 0 kg
Reason: First check the equations to check that the initial amount is 497 kg. You can do this by setting x = 0 into all of the equations. The 3rd and 4th equations evaluate to 2 when x = 0 and so you can eliminate the bottom 2 equations immediately. Equation # 2 does not work since the half-life value of 1.040 kg is way to small (significantly smaller than half of 497 kg).
You can check that equation # 1 is the right one, by setting x = 0 and getting
y = 497*(1/2)^[(1/38) * 0] = 497
so the initial amount is 497
Also check that there is 1/2 the amount at time 38 (since the half-life is 38 days)
y = 497 * (1/2)^[(1/38) * 38] = 248.5
248.5 kg is half of 497 and so this checks out for equation # 1.
Since we know equation # 1 is good, now we evaluate at x = 4 to get
y = 497 * (1/2)^[(1/38) * 4] = 462.029
so our answer to the thousandth places is 462.029 kg.
