I\'m given two values for time and temperature at that specific time. I also hav

Question

I'm given two values for time and temperature at that specific time. I also have an initial temperature. I do not have a value for my constant k, or for the environment's temperature. I do not think I have enough information to solve for one or the other. I am given an initial temperature of 70 degrees F, and for T(1/2 minute) = 110 degrees F and for a full T(1 minute) = 145 degrees F. I'm not looking for an answer, I just need help reworking the equation T(t) = Tm + (T(0)-Tm)*e^(kt) to solve for k first.

Explanation / Answer

There are three unknowns in the equation T(t) = Tm + (T(0)-Tm)*e^(kt) that is T(0),Tm,k. To solve for these three variables, we require 3 equations. 1. T(0) = 70 F 2. T(1/2 min) = 110 F 3. T(1 min) = 145 F. 110 = Tm + (70-Tm) e^(30k) 1/2 min =30 sec 145 = Tm + (70-Tm) e^(60k) (110-Tm)/(70-Tm) = e^(30k) (145-Tm)/(70-Tm) = e^(60K) = e^(2*30K) = [e^(30k)]^2 = {(110-Tm)/(70-Tm)}^2 From the above equation we can get Tm and substituting for Tm in any of the above equation yields k

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