This document discusses using mathematical models to represent the thawing of frozen turkeys. It introduces logarithmic functions as a model for thawing curves, as the temperature increases over time in a way similar to the inverse of an exponential cooling curve. The document provides guidelines from the USDA for safely thawing turkeys either in the refrigerator over several days or in a water container over several hours, and shows how to construct a logarithmic model to fit starting and ending temperature points for a turkey thawing in the refrigerator.

1. Math in the News
Thanksgiving Temps

2. What You Will Learn
• Summary
– In this issue of Math in the News we look
at graphs representing the thawing of a
frozen Thanksgiving turkey.
• Define graphs of cooling curves
• Explore graphs of warming curves
• Model data using logarithmic
functions

3. Cooling Curves
• You’re probably more familiar with
cooling curves, which can be
modeled by decreasing exponential
functions.

4. Thawing Curves
• The situation with a frozen turkey is
different. You start with a
temperature below freezing and want
to reach a higher temperature.

5. Mathematical Modeling
What mathematical model can be used to show the thawing
of a turkey?
Discuss as a class how you would model this temperature
increase.

6. Thawing Curves
• It turns out that a reasonable model
for the reverse of cooling is the
inverse of the exponential, an
increasing logarithmic function.

7. Thawing Curves
• The USDA suggests two methods for
thawing a turkey:
– Thawing it in a refrigerator
– Thawing it in a container of water
• You must AVOID thawing a turkey at
room temperature on a counter. The
reason is that bacteria can form on
the thawed parts long before the rest
of the turkey has thawed.

8. Guideline for Thawing a Turkey
Refrigerator
• Whole turkey:
– 4 to 12 pounds — 1 to 3
days
– 12 to 16 pounds — 3 to 4
days
– 16 to 20 pounds — 4 to 5
days
– 20 to 24 pounds —5 to 6
days
Container of Water
• Whole turkey:
– 4 to 12 pounds — 2 to 6
hours
– 12 to 16 pounds — 6 to 8
hours
– 16 to 20 pounds — 8 to 10
hours
– 20 to 24 pounds — 10 to
12 hours

9. Thawing Curves
• We’ll use the USDA guidelines to
build a logarithmic function to model
the thawing of a frozen turkey.
• What you’ll need:
– A graphing calculator, preferably one that
has variable sliders
– Thermometer
– Spreadsheet for gathering data

10. Thawing Curves: Step 1
• Pick a method for thawing. Identify
the method your family will be using
to thaw the Thanksgiving turkey.
• For this example, let’s use the
refrigerator method to thaw a 12-
pound turkey over 3 days. Use these
data points as the start and end
points for the data:
(0, -10) and (3, 35)
At time 0, the temperature is -10°F.
After 3 days the temperature is 35°F.

11. Thawing Curves: Step 2
• Graph the start and end points on
your graphing calculator.

12. Thawing Curves: Step 3
• On your graphing calculator, set up a
logarithmic function of the form:
• Make sure that the values for a, b,
and c are tied to slider values on your
graphing calculator. With sliders you
can try endless values for a, b, and c
and see the impact on the graph.
y = a × log(b • x) + c

13. Thawing Curves: Step 4
• Manipulate the sliders until you find a
logarithmic function that fits the end
points. (There are an endless number
possible.)

14. Thawing Curves: Step 5
• Use the Trace feature to generate a
table of values. Use these to compare
predicted values from the model to
measured values.