The half-life of a substance is how long it takes for half of the substance to decay or become harmless (for certain radioactive materials). The half-life of a substance is 123 days and there is an amount equal to 150 grams now. What is the expression for the amount A(t) that remains after t days, and what is the amount of the substance remaining (rounded to the nearest tenth) after 365 days?
Hint: The exponential equation for half-life is A(t) = A0(0.5)t/H, where A(t) is the final amount remaining, A0 is the initial amount, t is time, and H is the half-life.

Question

The half-life of a substance is how long it takes for half of the substance to decay or become harmless (for certain radioactive materials). The half-life of a substance is 123 days and there is an amount equal to 150 grams now. What is the expression for the amount A(t) that remains after t days, and what is the amount of the substance remaining (rounded to the nearest tenth) after 365 days?
Hint: The exponential equation for half-life is A(t) = A0(0.5)t/H, where A(t) is the final amount remaining, A0 is the initial amount, t is time, and H is the half-life.

ginabean819 · Answer

A(t) = 150(0.5)t/123, 19.2 grams remaining
 A(t) = 150(0.5)123t, 1.4 grams remaining
 A(t) = 123(150)(0.5)t, 0.0 gram remaining
 A(t) = 150(0.5)123/t, 118.8 grams remaining

wolf1728 · Answer

That equation needs to be made a little bit easier to read: 
(and Formula Attached).
ending amount = (beginning amt)*[.5^(time/half-life)] 
ending amount = (150)*[.5^(365/123)] 
ending amount = (150)*[.5^2.9674796748] 

I think you can finish it from there.