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

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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

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

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But, you can estimate obviously that it's about 70
okay
You need an esquation to solve this...i think
Imma work this out first. (:
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.
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.
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
obviously, the ratio of the geometric series that gives the total number of cents on a particular day is 2.
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)
I think... ><'' not very expertise on this but had hw on this like 2 wks ago.
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
are we done with the question christine
The equation would be: 2^x-1, where x represents the day. substitute 7 for x and you have your answer
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
I am sorry, 2^(x-1)
there you go x3
So...basically do the same for each day doubling it
is the question whole finish
5 2^5-1 = 18-1 = 17 and so forth
is the answer finish now christine
thank you christine

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