Logarithmic

[Dave J]

Im stuck on this study question.

It says.

Iodine-135 has a half life of 8 days. How long would it take for 28kg of iodine-135 to decay to 200g?

The answer s 57.03 days.

Could someone explain how this answer was gotten? The unit is logarithmic funtions so I assume that they are involved, but how?

 

[galactus]

The formula for half-life is given by:

\(\displaystyle \L\\T=\frac{-1}{k}ln(2)\)

\(\displaystyle \L\\8=\frac{-1}{k}ln(2)\)

Solve for k, then use:

\(\displaystyle \L\\200=28000e^{kt}\)

and solve for t.