Question

Bill has a fifty billion dollar.
you have a dollar.
your money become 2 times larger than a year before. (ex: 1->2->4->8->...)
How long year does it take that yours is more than Bill's.
give me an answer without calculator.

Answer 1

I will keep track of my places here so i dont lose place.

Answer 2

128 7 Years

Answer 3

1024 10 years

Answer 4

4096 12 Years

Answer 5

8192 13 Years

Answer 6

16384 14 Years

Answer 7

Sorry if its taking me time im switching between two questions and my work

Answer 8

Can't you just do

\(\large 2^x \ge 50000000000\) ? since x = 0 would be 1 and x = 1 would be 2 etc...

Answer 9

32768 15 Years

Answer 10

Yes but if you dont do it in order and just put a inequality then it wont work because a inequality can be any number that would work

Answer 11

And it would be \[2n > 50000000000\]

Answer 12

It doesnt say equal to or greater than it says greater than

Answer 13

Now let me finish my math please

Answer 14

Right^ but adding the "equal to" will allow us to know when to stop...meaning when we see that x = 35.54 we can obviously say it will take 36 years to be more than Bill's

Because as you said...just Greater than..could be any number

Answer 15

John you have successfully ruined my day. I had one goal and now its ruined.

Answer 16

2^n=5000000000
log2^n=log5*10^9
nlog2=log5+9log10
n=(log5+9)/log2
so n should be greater than (log5+9)/log2, 32.22years

Answer 17

Or you could do it my way...

Answer 18

@eazykang WE'RE TALKING ABOUT YEARS NOT MONTHS SO IT'S MUST BE A NATURAL NUMBER

Answer 19

Dont yell man its just a number

Answer 20

in that case u can write 33 years

Answer 21

btw did question provide log 5 and log 2?
or else i think it cannot be solved without using calculator

Answer 22

Why not?

Answer 23

I was doing it without calcutlator until i was ruined

Answer 24

Now if you dont mine i will continue

Answer 25

65536 16 Years

Answer 26

131072 17 Years

Answer 27

262144 19 Years

Answer 28

524288

Answer 29

20 Years

Answer 30

1048576 21 Years

Answer 31

209722 22 Years

Answer 32

Thanks for the medal sorry i didnt finish it i had lunch

Answer 33

419444 23 Years

Answer 34

828888 24 Years

Answer 35

838888 sorry typo

Answer 36

165776 25 Years