Question

Beginning with 23 grams of a radioactive element whose half-life is 45 years, the mass y (in grams) remaining after t years is given byy = 23(1/2)^t/45, t ≥ 0.How much of the initial mass remains after 170 years? (Round your answer to three decimal places.)

Answer 1

`y\approx1.677g`

1) As we were told of the half-life formula along with the data, we can write out the following to get the remains after 170 years:

`\begin{gathered} y=23((1)/(2))^{(t)/(45)} \\ y=23((1)/(2))^{(170)/(45)} \\ y=23((1)/(2))^{(170)/(45)}^ \\ y\approx1.677 \end{gathered}`

2) So, according to this model we can tell there will be left approximately

`1.677g`