SOLUTION: IF YOU EARN $1 THE FIRST DAY OF WORK AND YOU SALARY IS DOUBLE EVERY DA1 (I.E. 1,2,4,8,16,32)HOW MUCH WILL YOU HAVE EARNED AFTER 30 DAYS?

Algebra ->  Equations -> SOLUTION: IF YOU EARN $1 THE FIRST DAY OF WORK AND YOU SALARY IS DOUBLE EVERY DA1 (I.E. 1,2,4,8,16,32)HOW MUCH WILL YOU HAVE EARNED AFTER 30 DAYS?      Log On


   

Question 73431: IF YOU EARN $1 THE FIRST DAY OF WORK AND YOU SALARY IS DOUBLE EVERY DA1 (I.E. 1,2,4,8,16,32)HOW MUCH WILL YOU HAVE EARNED AFTER 30 DAYS?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
This is a geometric progression. Every term is double the preceding term. Most beginning
math books will derive and show you the equation for the sum of the terms in a geometric
progression.
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This equation is:
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S+=+%28a%281-r%5En%29%29%2F%281-r%29
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where the variables are defined as:
S = the sum of the terms in the given progression
a = the first term. In this problem the first term is 1
r = the common ratio. In this problem the common ratio is 2 (terms are doubled)
n = the number of terms. In this problem n = 30
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Let's now just substitute numbers for this problem into the equation for the sum to get:
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S+=+%281%281-2%5E30%29%29%2F%281-2%29
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We can eliminate the multiplier 1 in the numerator, and the denominator becomes -1.
With these two changes the problem becomes:
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S+=+%281-2%5E30%29%2F%28-1%29+=+-%281-2%5E30%29+
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A calculator will tell you that 2%5E30+=+1073741824. Substituting this results in:
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S+=+-%281-1073741824%29+=+-%28-1073741823%29+=+1073741823 dollars
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Not a bad deal. Start with a dollar on day 1 and 30 days later be worth $1,073,741,823.
A billionaire in just a month.
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Hope this helps you see how to work the problem.