SOLUTION: 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 th

Algebra ->  Sequences-and-series -> SOLUTION: 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 th      Log On


   

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.
Answer by htmentor(1343) About Me  (Show Source):
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).
The job that pays $1000 earns you 100000 pennies.
Is there a day (n<30) in which you start to earn more than 100000 pennies?
2^(n-1) = 100000 = 10^5
log10(2^(n-1)) = log10(10^5)
(n-1)log10(2) = 5
n = 5/log10(2) + 1
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.
Take the penny-doubling job...