Once a certain medicine is in the bloodstream, its half-life is 21 hours. How long will it be before an initial 30cc of the medicine has been reduced to 7cc?

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Answer 1 · 2016-11-18T23:43:03

Here is the formula given by my teacher to solve this problem.

$y=Ab^(t/k)$

A represents the initial amount, in this case, it is 30cc

B is the base, half-life is always 1/2

And t represents time, we are told that it half every 21 hours, hence it should be $t/21$

$7cc = 30cc*(1/2)^(t/21)$

$(7/30) = (1/2)^(t/21)$

$log(7/30) = (t/21) log (1/2)$

$log(7/30)/log (1/2) = (t/21)$

$t = 44.09$

The answer is round to two decimal places.