SOLUTION: A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a table in a room where the temperature is 75 Fahrenheit. a). If the temp

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Question 1112016: A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a table in a room where the temperature is 75 Fahrenheit.
a). If the temperature of the turkey is 141 Fahrenheit after half an hour, what is its temperature after 45 minutes?
b). When will the turkey cool to 100 Fahrenheit?
Answer by MathTherapy(10801) About Me  (Show Source):
You can put this solution on YOUR website!
A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a
table in a room where the temperature is 75 Fahrenheit.

a). If the temperature of the turkey is 141 Fahrenheit after half an hour, what is its temperature after 45 minutes?

b). When will the turkey cool to 100 Fahrenheit?
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You can use Newton's Law of Cooling.......any of the following 3 formulae should work: 

This author's preference is the 1st formula. In this case, the cooling rate (k) is first needed, and is derived as follows:

       , where: t = time taken to get to a COOLED temperature (1%2F2 an hr, or 30 minutes, in this case)
                                             T%28t%29 = TEMPERATURE (T) at a given time (t)___(141oF, in this case) 
                                              T%5Bs%5D = SURROUNDING Temperature (75oF, in this case)
                                              T%5Bo%5D = ORIGINAL/INITIAL temperature (185oF, in this case)
                                               k = the CONSTANT or COOLING rate (UNKNOWN, in this case)
                                      
                                       ---- Substituting 30 for t, 75o for T%5Bs%5D, and 185o for T%5Bo%5D
                                          matrix%281%2C3%2C+141%2C+%22=%22%2C+75+%2B+%28185+-+75%29+%2A+e%5E%28-+30k%29%29 ----- Substituting 141o for T(30)
                                          
                                       matrix%281%2C3%2C+-+30k%2C+%22=%22%2C+ln+%283%2F5%29%29 ----- Converting to NATURAL LOGARITHMIC (ln) form
                                              matrix%281%2C5%2C+k%2C+%22=%22%2C+ln%283%2F5%29%2F%28-+30%29%2C+%22=%22%2C+.01702752%29
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a). If the temperature of the turkey is 141 Fahrenheit after half an hour, what is its temperature after 45 minutes?

                                                           
                                                            ---- Substituting 45 for t, 75o for T%5Bs%5D, 185o for T%5Bo%5D,          
                                                                                                                                               and .01702752 for k
Temperature, after 45 minutes, or , or approximately 126oF.
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b). When will the turkey cool to 100 Fahrenheit?

                                                           
                                                                matrix%281%2C3%2C+100%2C+%22=%22%2C+75+%2B+%28185+-+75%29+%2A+e%5E%28-+.01702752t%29%29 ---- Substituting 100 for T(t), 75o for T%5Bs%5D, 185o for T%5Bo%5D,
                                                                                                                                            and .01702752 for k
                                                        
                                             matrix%281%2C3%2C+-+.01702752t%2C+%22=%22%2C+ln%285%2F22%29%29 ---- Converting to NATURAL LOGARITHMIC (ln) form
Time taken for the turkey to cool to 100oF, or