help please math..............?

Question

suppose you earned $1on your first day @ work, $2 the second day, $4 on the third, $8 on the fourth day and so on. how much would your total earnings be on the 15th day?

Answer 1

Total Earnings Would be:

2^0+2^1+2^2+2^3+...2^13+2^14

=$32,767

Answer 2

Hi.

The summation of Xn over n=0 to n=14, where x = 2^n i.e. the number 2 to the power n. For example,

Total earned = x0 + x1 + ..... + x14
= 2^0 + 2^1 + .... + 2^14
= 1 + 2 + .... + 16384
= I'll let you add it up. But I think it is (2^15) - 1

But basically, for any duration starting at day X and ending on day Y, you take take the summation of 2^n (2 to the power of n) from n=X to n=Y.

I hope this helps. If you have a calculator, it will most likely have a summation function.

-Leon S

Answer 3

on each day you earn twice as much as you did the day before. On the first day, you earn 2^0=1, on the second, 2^1 = 2, on the third, 2^2=4, and so on. So on the 15th, you earn 2^14 dollars, which comes to $16,384.

Answer 4

this is a geometric series:
1,2,4,8,16.... and so on.

the sum rule of the geometric series is :

S = { a[ (r^n) -1 ] } / ( r-1)

where r is the ratio between each two terms, a is the first term and n is the last term.
r =2 because each term is multiplied by 2 in order to get the next term.
a= 1, and n=15.
so:
S = { 1 [ (2^15) -1 ] } / (2-1) = [(2^15) -1 ] /1 = (2^15) -1
= 32768 -1 = 32767
so the answer is $32767 total after 15 days.

Answer 5

Each day you make twice as much as you did the previous day, so:
Day Earnings
1 $1
2 $2
3 $4
4 $8
5 $16
6 $32
7 $64
8 $128
9 $256
10 $512
11 $1024
12 $2048
13 $4096
14 $8192
15 $16384

Add all this up, and you get a total of $32767

Answer 6

Well if you want to know the earnings of just the fifteenth day then the answer would be $16784. But if you wanted to know how much money you would earn the first fifteen days all added together, then the answer would be $33467.

Answer 7

simple...

it is adding: 1+2+4+8+...+ = 1+2^1 + 2^2 + 2^3 + ... + 2^14

the formula for 1+2^1+2^2+.....+2^n = 2^(n+1) - 1

hence the sum is 2^15-1 (n=14)

exercise:

just add terms and check (like this: 1, 1+2, 1+2+4, 1+2+4+8...)... what pattern do you observe?

without using formula you can do like this:

let S = 1+2^1 + 2^2 + 2^3 + ... + 2^14
so 2S = 2+2^2 + 2^3 + ... + 2^15

subtracting (2S-S) we get S = 2^15 - 1 (other terms will cancel out...do this and check)

note: 2^15 is 32*32*32 (since 32=2^5)

Answer 8

It's simple, just double your earnings everyday and finally add it all up. You might wanna use a calculater. That's my only advice. Sorry but I can't do your work for you. Good Luck Though!

Answer 9

its sunday
i dont do math on sundays
but i do have to do math home work
perhaps i will do math on sunday
perhaps not
it all depends on how i feel
u kno what i mean?
and i think after im done with my math i will have dinner and maybe a bowl of ice cream
maybe for dinner i shall have mcdonalds
i wonder how those new snack wraps are
have u had them?
they look good
r they big or small?
maybe ill have a snickers mcflurry to go along with it
and yeh
im prolly gonna watch fox tonite to
and then do my math
it all dpends on how i feel
well im gonna go now
but maybe i will keep answering this question
perhaps i shall keep typing
well maybe perhaps not
it all depends on how i feel
u know what i mean?

Answer 10

I agree with Steven Jay give him the points