Question

Isabella save 2 nickels today, if she doubles the number of Nicole, she saves every day, how many days, including today, will it take her to save more than 500 nickels?

Answer 1

Answer:

  8 days

Step-by-step explanation:

On day 8, Isabella will save 256 nickels, bringing her total to 510.

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The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.

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The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.

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The number of nickels saved on day n is a geometric sequence with first term 2 and common ratio 2. The n-th term of the sequence is ...

  an = a1·r^(n-1) = 2·2^(n-1) = 2^n

The sum of n terms of the sequence is ...

  S = a1(r^n -1)/(r -1) = 2(2^n -1)/(2-1)

  S = 2^(n+1) -2

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We want S > 500, so ...

  500 < 2^(n+1) -2

  502 < 2^(n+1)

  251 < 2^n

  log(251) < n·log(2)

  n > log(251)/log(2)

  n > 7.97 . . . . . . . . 8 days or more to save more than 500 nickels