SOLUTION: My uncle has 6 million dollars to spend. On the first day he spent $1, on the second day he spent $2, on the third day he spent $4, and so forth with the amount doubling every day

Question 1028128: My uncle has 6 million dollars to spend.
On the first day he spent $1, on the second day he spent $2, on the third day he spent $4, and so forth with the amount doubling every day.
If he continues to spend every day, how long will his 6 million dollars last?
Answer by jorel555(1290) (Show Source): You can put this solution on YOUR website!
Let's use the first 4 days. Your uncle will have spent:
1+2+4+8=15
15+1=16=2^4
Similarly, for five days we have:
1+2+4+8+16=31
31+1=32=2^5
Generalizing, it is apparent that the sum of 2^0+2^1+2^2+....+2^n=2^n+1
If we want to spend 6 million dollars, then:
2^n+1=6000000
2^n=5999999
n, in this case, is somewhere between 2^22 and 2^23, so his money will last only until shortly after the 22nd day!!!!!!!!!!!!!
RELATED QUESTIONS
Sam was remodeling his house on the first day he bought 5 feet of fence post and 4 feet... (answered by LinnW)

Daniel wants to save at least 20 dollars by putting pennies in a jar each day. On the... (answered by richwmiller)

An investigator has a 430 page report to read. The first day, he is able to read 20... (answered by ewatrrr)

Shawn read one fifth of the book on the first day. On the second day he read 12 pages. On (answered by ewatrrr)

Elijah spent 5.25 for lunch every day for 5 days. He spent 6.75 on Saturday. How much did (answered by ewatrrr)

Josh started a new job. On his first day, he makes $20. On his third day, he makes $12.... (answered by ikleyn,josgarithmetic)

On the first day, Nabil put $1 in a big box. Then, each succeeding day, he added to the... (answered by Alan3354)

Omar swam on each of three days. He swam three times as far on the second day as he did... (answered by mananth)

A man starts saving on 1st November, he save Shs 1 the first day,Shs.2 on second day... (answered by fractalier)