document.write( "Question 873559: Which would you rather have: A job that pays $1000 for 30 days or a job that pays you a penny on the first day, 2 pennies on the second day, 4 pennies on the third, 8 pennies on the forth and continues each day for 30 days? Show mathematical evidence to support your answer. \n" ); document.write( "

Algebra.Com's Answer #526986 by htmentor(1343) $\"\"$ $\"About$

You can put this solution on YOUR website!
The amount of money you earn (in pennies) on the n-th day will be 2^(n-1).
\n" ); document.write( "The job that pays $1000 earns you 100000 pennies.
\n" ); document.write( "Is there a day (n<30) in which you start to earn more than 100000 pennies?
\n" ); document.write( "2^(n-1) = 100000 = 10^5
\n" ); document.write( "log10(2^(n-1)) = log10(10^5)
\n" ); document.write( "(n-1)log10(2) = 5
\n" ); document.write( "n = 5/log10(2) + 1
\n" ); document.write( "This gives n = 17.6. So on the 18th day, you will already start earning more than the $1000, not even counting all the money you've earned up to that point.
\n" ); document.write( "Take the penny-doubling job... \n" ); document.write( "

\n" );