Question 1136353
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Scientists like to  write exponential decay functions using base e; and sometimes there are good reasons for that.  But with half life problems, it seems to me far easier to write the exponential decay function as<br>
A = I(1./2)^t<br>
where t is the number of half lives.<br>
In this problem, the half life is 4 days, and the stated period is 20 days.  That is an integer number of half lives; the solution is simple.<br>
20 days if 5 half lives; the original mass has been reduced by a factor of 2^5=32.  If 5g are left, the original amount was 5*32 = 160g.<br>
Note the other tutor, using e and natural logarithms, ended up with the wrong answer by transposing a couple of digits near the end of the calculations.<br>
The amount remaining after 4 weeks = 28 days = 7 half lives is the original 160g, reduced by a factor of 2^7 = 128 (or the amount remaining after 20 days, reduced by another factor of 2^2=4 for the 2 additional half lives).  That amount is 160/128 = 5/4 = 1.25g.