Question

Strontium- 90 is used in machines that control the thickness of paper during the manufacturing process. Strontium-90 has a half life of 28 years. Determine how much time has elapsed if the following percentage of a sample remains at 3.125%.

Answer 1

the formula for half-life is
\[\frac{\ln 2}{k} = t\]
where k is the decay constant and t is time

\[\frac{\ln 2}{t} = k\]
\[\frac{\ln 2}{28} = k\]

now use the formula for decay
\[\ln (\frac{x_o}{x}) = kt\]
\[\Large \frac{\ln (\frac{x_o}{x})}{k} = t\]
\[\Large \frac{\ln (\frac{x_o}{0.03125 x_o})}{\frac{\ln 2}{28}} = t\]

hehe lol

Answer 2

so basically \[\Large t = \frac{\ln (\frac{1}{0.03125})}{\frac{\ln 2}{28}}\]

Answer 3

i'll let satellite do his traditional correction now...

Answer 4

or maybe \[\left(\frac{1}{2}\right)^{\frac{t}{28}}=.0315\]
\[\frac{t}{28}=\frac{\ln(.0315)}{\ln(.5)}\]
\[t=\frac{28\ln(.0315)}{\ln(.5)}\]

Answer 5

no just a different (and i find much easier) method
since we are told the half life it is natural to use \(\frac{1}{2}\) as the base

Answer 6

well yours definitely looks neater...

Answer 7

lol yup they're the same :)