Question

Beginning with 25 grams of a radioactive element whose half-life is 45 years, the mass y (in grams) remaining after t years is given by
y = 25

1
2
t/45

, t ≥ 0.
How much of the initial mass remains after 130 years? (Round your answer to three decimal places.)

Answer 1

Step-by-step explanation:

the function for the given situation is

y = 25(1/2)^(t/45)

half-life means that after the given period of time (here 25 years) only half of the original mass is remaining.

after another period with the same length half of the mass from the end of the previous period is now only remaining.

and so on, and so on ...

therefore the function multiplies the original mass by a factor of 1/2 every 45 years (or the corresponding fraction of 45).

after 130 years we have

y = 25(1/2)^(130/45) = 3.375186684...

≈ 3.375 grams remaining.