Question 1191731
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Both responses you have received show the same right answer; but the calculations performed in each response are far more convoluted than what is necessary.<br>
You have 150mg of a substance decaying to 20mg in an unknown number of half-lives.  The equation is simple:<br>
{{{150((1/2)^n)=20}}}
{{{150/20 = 2^n}}}<br>
The variable is in an exponent, so use logarithms and use a calculator.<br>
{{{n*log(2)=log(7.5)}}}
{{{n = log(7.5)/log(2)}}}<br>
That number of half-lives, to several decimal places, is 2.90689.  Multiply that by the 5.27 years for one half life and you get the answer of approximately 15.32 years.<br>
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It should be noted that radioactive decay is a statistical process; after one half life the amount remaining is APPROXIMATELY half of the original.  So keeping 6 or 7 decimal places in the answer to a problem like this is unreasonable.<br>