Question

You start with $.50 at the beginning of the year. This amount doubles every month. How much will you have at the end of the 12th month? Careful: You have been asked to find the amount at the END of the month!! Begin by writing the rule for the sequence. (I have worked this out and at least understand a little of what i am doing here but i don't completely understand it.)

Answer 1

After the FIRST 12 months : doubles so 0.5*2
After the SECOND 12 months :Double of what you already have so 0.5*2*2
After the THIRD 12 months : Double of what you already have so 0.5*2*2*2

Answer 2

can you see the pattern..
After N 12 months:Double of what you already have so:????

Answer 3

yes! thank you :D
i see what happen now on my side, i appreciate it thanks.

Answer 4

okay sure, you are welcome!

Answer 5

another way to think about it is..
After N 12 months you hare double of N-1 12 months
for N-1 12 months you have double of N-2 12 months
N-2 12 months you have double of N-3 12 months
pattern goes on until
N-(N+1) 12 months you have double of N-N 12 months
since at the end we have N-N = 0 and we started with 0.5 there and double of that is 0.5*2=1 so there we have it
we subtracting -0 to begin with then -1 then -2.. upto -(N+1) which is atotal of N subtractions of -1
so... that means we doubles a total of N times so
Final answer for N 12 months you have 0.5*2^N
.. Kind of a silly/complicated way of going about something simple but this is what mathematicians do sometimes lol
a minute

Answer 6

You can just ignore that if it looks a bit complicated.. it introduces nice idea of recursion though

Answer 7

wow actually the way you just explained it seems a lot easier for me to understand with that i was able to understand it better sometimes it easier when said in other away.
Also i think i solved the problem when 0.5 x 2^12 and i continued i got the answer 2048.

Answer 8

thats great :) you will enjoy programming then

Answer 9

and yes umm I just realized this whole question i was thinking they said after every 12 months its doubled so after N 12 months... what will it be -.-
But they just said after every month, ugh i wrote a lotta 12 months in there for nothing, but I think you for the idea anyway lol.

Answer 10

sometimes my english skills scare even me

Answer 11

and yes umm I just realized this whole question i was thinking they said after every 12 months its doubled so after N 12 months... what will it be -.-
But they just said after every month, ugh i wrote a lotta 12 months in there for nothing, but I think you got** the idea anyway lol.

Answer 12

oh lol yeah but you know you were on the right track it was just you thought one thing while it said another cx but still it helped thank you, and yes i got the idea actually it was better explained and their is a way to check this answer i think im going to have to find it -.- probably something so easy ill just feel dumb for not realizing

Answer 13

but then 0.5 * 4096 would equal 2048

Answer 14

no 2048! is right

Answer 15

i just did it on my fingers lol

Answer 16

lol

Answer 17

\[since 0.5= 1/2 = 2^{-1}\\
and~\\ 0.5*2^{12}=2^{-1}*2^{12} = 2^{11}\]

since we have 10 fingers and not 11 start saying 4 on the first finger instead of 2
and start doubling on all your fingers till you reach the last finger :)

Answer 18

i dunno for some reason its hard to do it in your head.. to keep track of doubling numbers and then to think how many times you've doubled so far haha

Answer 19

i just tried it lol but wait so you use all 5 fingers and count 4 instead of two each one ok.
and oh i try all the time thinking i could do everything in my head in the end i lose to multitasking with multiple problems in my head -.-

Answer 20

no like this ill draw it wait