document.write( "Question 1096997: The half-life of zulus is 14 days and they decay exponentially. If Angela begins with 20 zulus, how long will it take until only 5 remain? \n" ); document.write( "

Algebra.Com's Answer #711502 by greenestamps(13200) $\"\"$ $\"About$

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Tutor jorell380 is almost certainly a scientist more than a mathematician; scientists like to work exponential functions using e as the base. For me, as a mathematician, working half life problems using powers of 1/2 makes far more sense.

\n" ); document.write( "For problems with half lives, the exponential decay function is
\n" ); document.write( " $\"y+=+A%2A%28%281%2F2%29%5Ex%29\"$

\n" ); document.write( "y is the amount remaining; A is the initial amount; and x is the number of half lives.

\n" ); document.write( "For your problem, we have 20 zulus to start and 5 at the end. So the number of half lives is found by solving the following equation for x:

\n" ); document.write( " $\"5+=+20%28%281%2F2%29%5Ex%29\"$
\n" ); document.write( " $\"1%2F4+=+%281%2F2%29%5Ex\"$
\n" ); document.write( "We don't need any logarithms there! 1/4 is (1/2)^2; it takes 2 half lives for the number of zulus to drop from 20 to 5.

\n" ); document.write( "The half life is 14 days, so 2 half lives is 28 days.

\n" ); document.write( "Answer: 28 days \n" ); document.write( "

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