Selena2345
  • Selena2345
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
So...
anonymous
  • anonymous
Um, I'm not so sure how to put this in an equation...
Selena2345
  • Selena2345
it is not an equation

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anonymous
  • anonymous
But, you can estimate obviously that it's about 70
Selena2345
  • Selena2345
okay
anonymous
  • anonymous
You need an esquation to solve this...i think
anonymous
  • anonymous
Imma work this out first. (:
anonymous
  • anonymous
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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
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
anonymous
  • anonymous
obviously, the ratio of the geometric series that gives the total number of cents on a particular day is 2.
anonymous
  • anonymous
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)
anonymous
  • anonymous
I think... ><'' not very expertise on this but had hw on this like 2 wks ago.
anonymous
  • anonymous
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
Selena2345
  • Selena2345
are we done with the question christine
anonymous
  • anonymous
The equation would be: 2^x-1, where x represents the day. substitute 7 for x and you have your answer
anonymous
  • anonymous
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
anonymous
  • anonymous
I am sorry, 2^(x-1)
anonymous
  • anonymous
there you go x3
anonymous
  • anonymous
So...basically do the same for each day doubling it
Selena2345
  • Selena2345
is the question whole finish
anonymous
  • anonymous
5 2^5-1 = 18-1 = 17 and so forth
Selena2345
  • Selena2345
is the answer finish now christine
Selena2345
  • Selena2345
thank you christine

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