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

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) (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...
RELATED QUESTIONS
what is the equation for this problem. A man has a job for thirty days, he will be paid 1 (answered by stanbon,Nate,Edwin McCravy)

Would you rather have a savings account that pays 5 % compounded semiannually or one that (answered by Alan3354)

Topics In Contemporary Math Exponential Growth 2) Which would you rather have, one... (answered by math_tutor2020,ikleyn,Alan3354)

MAT 145: Topics In Contemporary Math 17: Exponential Growth 2) Which would (answered by ankor@dixie-net.com)

Would you rather have a saving account that pays 5% interest compound semiannually or... (answered by checkley77)

Imagine you start saving pennies during summer vacation. On the first day, drop one penny (answered by Boreal,MathTherapy)

You are considering two job offers for selling TVs. Job A pays $300 plus $9.00 per hour (answered by Theo)

You are offered two different furniture sales jobs the furniture barn offers you a job... (answered by ewatrrr)

i have solved that if Worker A finishes a job in 8 days and worker B finishes it in 12... (answered by josmiceli)