Question 1129640
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I find the formula for radioactive decay easier to understand if we write it in terms of number of half-lives, instead of in terms of numbers of days (or hours, or years, or milliseconds).<br>
The amount of a radioactive sample remaining after n half-lives is the original amount, 250g, multiplied by 1/2 to the power n.<br>
{{{f(n) = 250(.5)^n}}}<br>
We are given that after 250 minutes the amount remaining is 32g.  Use that to find the number of half-lives there are in 250 minutes.<br>
{{{32 = 250(.5)^n}}}
{{{0.128 = .5^n}}}
{{{log((.128)) = n*log((.5))}}}
{{{n = log((.128))/log((.5))}}} = 2.9658 to 4 decimal places<br>
The half life is then<br>
{{{250/2.9658}}} = 84.2947 minutes to 4 decimal places<br>
The formula for the remaining amount as a function of the number of minutes t (with n = t/84.2947) is then<br>
{{{f(t) = 250(.5)^(t/84.2947)}}}