Complete the table given below.
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  see the attached table

Step-by-step explanation:

We assume the formula of interest is ...

  residual = (initial amount)(1 -k)^t . . . . . . assuming k is a positive number

Where T is the half-life, this formula can also be expressed as ...

  residual = (initial amount)(1/2)^(t/T)

Then the relationship between k and T is ...

  (1 -k)^t = (1/2)^(t/T)

or ...

  1 -k = (1/2)^(1/T)

This lets us write k in terms of T as ...

  k = 1 -(1/2)^(1/T)

and it lets us write T in terms of k as ...

  log(1-k) = (1/T)log(1/2)

  T = log(1/2)/log(1-k)

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The attached spreadsheet table implements these formulas to compute T from k and vice versa. Formatting is in % and to four decimal places as required by the problem statement.

the answer is 489

step-by-step explanation: