math question

If you were to plot this on a graph it would be an exponential curve and the formula for an exponential curve is y=a*(r)^x where a is the y intercept and r is the common ratio. To help you out, a is the original number you started with which was 1 cent and to find r all you have to do is divide the money you earned one day by the money you got the day before. So (4/2) or (2/1) which both equal 2 so that's your common ratio. Now that you have both a and r you plug them into your equation and you get y=1*2^x Y is the money you've gotten and x is the number of days you've worked there. Oh and by the way just so you don't get confused, day 1 would appear as 0 on the x axis, day 2 would be 1 and so on.

tanna.wirsch:

Find an equation for this question:

You get a new job and your contract is one month long. On the first day your boss invests 1cent into an account for you which pays 100% interest per day. (on the second you get 2c, on the third you get 4c) On the last day of work your boss will close the account and give you the balance.
Can you find an equation to find the amount in the account at any given day?

I just finished and i then realized that I had read the question wrong. I thought I was getting paid an extra 1 cent every day but I am not. I am only getting paid 1c once.
Oh well, I've done it now so i will leave it there.

My made up question: You get a new job and your contract is one month long. On the first day your boss invests 1cent into an account for you which pays 100% interest per day. (on the second you get 2c, on the third you get 4c) On the last day of work your boss will close the account and give you the balance. He invests another 1c each day that you work and it also accrues interest at 100% per day.

day
1 ......1
2 ......2 + 1
3.......4 + 2 + 1
4 ......8 + 4 + 2 + 1
5 .....16+ 8 + 4 + 2 + 1
...
d .....2 ^n-1 + 2 ^n-2 + ......+1

So on day n (after the 1c payment) you will have 1+2+4+8+ ......+ 2 ^d-1

As Walt said, this is a GP
a=1 r=2
[This is just the formula - S stands for Sum] S _n=a(r ⁿ-1) / (r-1)

S _d=1(2 ^d-1) / (2-1)

S _d= 2 ^d-1

So after d days I will have a total of 2 ^d-1 cents

To get a proper appreciation for this I will show you some earnings.

On the 10th day I will have 1023c or $10.23
On the 20th day I will have 1048575c or $10,485.75
On the 30th day I will have 1073741823 cents or $10,637,418.23
------------------------------------------------------------------------------------------------------------------------------------
I've finished now and I just realized that I misread the question. I thought I was getting paid an extra 1 cent every day but I am not. I am only getting paid 1c once.
What a cheap skate boss! Now I will have to start again.

Original Question: You get a new job and your contract is one month long. On the first day your boss invests 1cent into an account for you which pays 100% interest per day. (on the second you get 2c, on the third you get 4c) On the last day of work your boss will close the account and give you the balance.

[size=150]Walt was completely correct.[/size] On day d you will have 2 ^(d-1) cents or 2 ^(d-1)/100 dollars

On the 10th day I will have $5.12
On the 20th day I will have $5242.88
On the 30th day I will have $5,368,709.12

I would have rather had the 10.6 million dollars, not just a measely 5.3 million. What a disappointment!

This is the graph that Walt was talking about.
140121 Payment.JPG