HELP!!!!!!! The half-life of a specific radioactive compound is 20 years. The equation used to model this half-life is y = 5 (1/2) t/20 where t represents time. Currently, there are 5 pounds of this compound 15 feet below the earth's surface. When will there only be 4 pounds of this compound left? Round your answer to the nearest tenth of a year.

Question

HELP!!!!!!! The half-life of a specific radioactive compound is 20 years. The equation used to model this half-life is  y = 5 (1/2) t/20 where t represents time. Currently, there are 5 pounds of this compound 15 feet below the earth's surface. When will there only be 4 pounds of this compound left? Round your answer to the nearest tenth of a year.

anonymous · Answer

You should have written "t represents time in YEARS."

4 = 5(0.5)^(t/20) → 4/5 = (0.5)^(t/20)

Log(0.8) = Log((0.5)^(t/20)) = (t/20)Log(0.5) 

So, t = 20Log(0.8)/Log(0.5) = 6.44 years = about 6 years 5 months 8 days