SOLUTION: On the first day Juanita receives 1 dollar. On each succeeding day, she receives 1 dollar more than the total received in all preceding days. On which day will she first receive an

Algebra ->  Sequences-and-series -> SOLUTION: On the first day Juanita receives 1 dollar. On each succeeding day, she receives 1 dollar more than the total received in all preceding days. On which day will she first receive an      Log On


   

Question 206743: On the first day Juanita receives 1 dollar. On each succeeding day, she receives 1 dollar more than the total received in all preceding days. On which day will she first receive an amount greater than one hundred dollars?
(A) 6th day (B) 7th day (C) 8th day (D) 9th day (E) 10th day
Answer by stanbon(75887) About Me  (Show Source):
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): On the first day Juanita receives 1 dollar. On each succeeding day, she receives 1 dollar more than the total received in all preceding days. On which day will she first receive an amount greater than one hundred dollars?
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1st day 1 = 2^0
2nd day 2 = 2*1
3rd day 4 = 2^2
...
nth day 2^(n-1)
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You want to know what the smallest n is that will produce 2^(n-1)> 100
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Equation: 2^(n-1) = 100
Take the log of both sides to get:
(n-1)log(2) = log(100
(n-1) = log(100)/log(2)
n-1 = 2/log(2) = 6.644
n = 7.644
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She will receive more than 100 on the 8th day and beyond.
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Cheers,
Stan H.
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(A) 6th day (B) 7th day (C) 8th day (D) 9th day (E) 10th day