calc

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The half-life of polonium is 139 days, but your sample will not be useful to you after 95 % of the
radioactive nuclei present on the day the sample arrives has disintegrated. For about how many days
after the sample arrives will you be able to use the polonium?

you want to know when you have 5% left.

Let P = c(2)^(-t/13), where c is the amount you started with, and t is the number of days.

so we want .05c=c(2)^(-t/139)

I used logs to solve and got t = 600 days

  • calc -

    t=139ln(.05)/(ln(1/2))

    t=139ln(.05)/(ln(1)-ln(2))

    t=139ln(.05)/(0-ln(2))

    t=139ln(.05)/(-ln(2))=600.7480052=600 days

    t=(half life* ln(percent of sample left))/(ln(1/2))

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