Question

the number of cells in a sample doubles every minute. A doctor with a sample of 25 cells and predicted that, after 5 minutes, he would have 32 cells. Is his prediction reasonable? Explained​

Answer 1

Answer: No, his prediction is unreasonable. After 5 minutes, the number of cells would be 400, not 32. See the explanation below for details.

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Remember:

• 
  `a_(n)` =
  `n`th term
• 
  `n` = number of terms
• 
  `a_(1)` = first term
• 
  `r` = common ratio

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Identify the given information.

`a_(1)` = 25

`r` = 2

Use the explicit formula for geometric sequences.

`a_(n) = a_(1) r^(n - 1)`

Substitute the given values.

`a_(n) = (25)(2)^(n - 1)`

Substitute in 5 for
`n` to find out how many cells there would be after 5 minutes.

`a_(5) = (25)(2)^(5 - 1) \\\\a_(5) = (25)(2)^(4) \\\\a_(5) = (25)(16)\\\\a_(5) = 400`