Question

WILL mark brainliest!

Answer 1

Answer:

  110.5348 minutes

Step-by-step explanation:

The difference from room temperature changes from 103 to 59 in 46 minutes, so that difference can be modeled by the exponential equation ...

  Δt = 103×(59/103)^(t/46)

We want to find t for the temperature difference Δt = 91 -64 = 27.

  27 = 103×(59/103)^(t/46)

  27/103 = (59/103)^(t/46) . . . . . divide by 103

Taking logs gives the linear equation ...

  log(27/103) = (t/46)log(59/103)

Multiplying by the inverse of the coefficient of t, we get ...

  t = 46·log(27/103)/log(59/103) ≈ 46·(-0.58147346)/(-0.24198521)

  ≈ 110.5347

It will take about 110.5347 minutes for the turkey to cool to 91 °F internally.

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Comment on 4 decimal places

An answer correct to 4 decimal places (7 significant digits) is a pretty good indication that the problem was worked correctly. However, that level of precision in the timing makes little sense in this context. Most thermometers will take at least a few seconds to register the temperature to within a tenth of a degree or so. This problem is asking for an answer that is within 6 milliseconds and 30 micro-degrees. Neither of these is anywhere near realistic for a kitchen meat thermometer.

More realistic would be an answer to 4 significant figures, a tenth of a minute and a few hundredths of a degree.

(The rate of change at the time of interest is about -0.33 degrees per minute.)