## Selena2345 3 years ago A Goblin Miner earns 1 cent the first day, 2 cents the second day 4 cents the third day, 8 cents the fourth day and so on doubling the amount each day. How much will the miner earn in 7 days ? 2 Weeks? 1 Month ( Make An Estimate Before Solving) Show/ Explain All Work

1. satellite73

7 days is easy 1+2+4+8+16+32+64

2. satellite73

you might notice that this is 127, one less than 2 times 64

3. satellite73

you have \(1, 2, 2^2, 2^3, 2^4, ...\)

4. Selena2345

5. satellite73

in 7 days you will have earned \(2^7-1=\\$1.27\)

6. Selena2345

7. satellite73

in two weeks you will have \(2^{4}-1\) pennies, a calculator gives \(\\$163.83\)

8. CliffSedge

I want that job if I get to work the whole month!

9. satellite73

me too in one month of 31 days you will have made \(2^{31}-1\) pennies, more money than i will earn in several life times

10. Selena2345

can u help cliffSedge

11. Selena2345

yes cliffsedge thank you

12. CliffSedge

If you have a calculator, you can try entering '1' then hitting x2 a bunch of times (counting how many times you do so.)

13. CliffSedge

Of course, that will only get you the per day earnings. You'll have to add up all the previous days' to get the total.

14. CliffSedge

But satellite's formula is a lot quicker. ;-)

15. Selena2345

thank you agent47

16. Agent47

Let x be the amt u earn per day... Then, in 1 day: 1cent = 2^0 cents 2 days: 2 cents = 2^1 cents 3 days: 4 cents = 2^2 cents 4 days: 8 cents = 2^3 cents... So, in n days, you get 2^(n-1) cents

17. Agent47

I think, satellite's made a mistake.. but that's IMPOSSIBRU!

18. Agent47

Thus, in 7 days: 2^(7-1)=2^6=64 cents

19. Agent47

woah waitttt

20. Agent47

That is the amount he earned on the 1st, 2nd, 3rd, 4th, etc days, and on the 7th day he earns 64 cents

21. Selena2345

is the answer to the question finish

22. Agent47

Not yet... the formula is: |dw:1347412596200:dw|

23. satellite73

actually i gave the total earned on day \(n\) not the amount earned on day \(n\)

24. Agent47

ya you're right, i just realized that

25. Selena2345

is the answer to the question finish

26. satellite73

on day \(n\) you earn \(2^{n-1}\) pennies, for a total of \(2^n-1\) pennies

27. Agent47

ok i see, then that's the final answer... satellite why are u so smart?

28. Selena2345

who's correct satellite or agent47

29. Agent47

satellite, obv, who's a level 100 here?

30. Agent47

but i did realize my mistake, before satellite pointed it out :P

31. Selena2345

who's correct satellite or agent47