Question

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

Answer 1

So...

Answer 2

Um, I'm not so sure how to put this in an equation...

Answer 3

it is not an equation

Answer 4

But, you can estimate obviously that it's about 70

Answer 5

okay

Answer 6

You need an esquation to solve this...i think

Answer 7

Imma work this out first. (:

Answer 8

We see that the series whose sum gives the total number of cents follows a regular pattern: each new term added to it is a power of two. This is an example of a geometric series.

Answer 9

In our case, we are told that the number of cents given each day is double the number given the day before, which suggests that the ratio of this series is 2.

Answer 10

no. pennies given on second day 2
------------------------------- = 2
no. pennies given on first day 1


no. pennies given on third day 4
------------------------------- = 2
no. pennies given on second day 2


no. pennies given on fourth day 8
------------------------------- = 2
no. pennies given on third day 4

Answer 11

obviously, the ratio of the geometric series that gives the total number of cents on a particular day is 2.

Answer 12

we can use the fact that the sum of a geometric series (called S) with n terms whose ratio is r is this
S = (first term)(1-r^n)/(1-r)

Answer 13

I think... ><'' not very expertise on this but had hw on this like 2 wks ago.

Answer 14

This means that for our series with a first term of 1 and a ratio of 2, we find the sum after n days

= 1(1 - 2^n) / (1 - 2)
= - (1 - 2^n)
= 2^n - 1

Answer 15

are we done with the question christine

Answer 16

The equation would be: 2^x-1, where x represents the day. substitute 7 for x and you have your answer

Answer 17

1 2^1-1 = 2-1 = 1
2 2^2-1 = 4-1 = 3
3 2^3-1 = 8-1 = 7
4 2^4-1 = 16-1 = 15

Answer 18

I am sorry, 2^(x-1)

Answer 19

there you go x3

Answer 20

So...basically do the same for each day doubling it

Answer 21

is the question whole finish

Answer 22

5 2^5-1 = 18-1 = 17 and so forth

Answer 23

is the answer finish now christine

Answer 24

thank you christine