SOLUTION: I need help with this homework question: You are cooking chili. When you take it off the stove, it has a temperature of 205 degrees F. The room temperature is 68 degrees F and t

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I need help with this homework question: You are cooking chili. When you take it off the stove, it has a temperature of 205 degrees F. The room temperature is 68 degrees F and t      Log On


   

Question 718211: I need help with this homework question:
You are cooking chili. When you take it off the stove, it has a temperature of 205 degrees F. The room temperature is 68 degrees F and the cooling rate is r=0.03 . How long will it take to cool to a serving temperature of 95 degrees F?
T= (T0 - TR)e^-rt + TR
T= cooling time in minutes
T0= initial temperature
TR= room temperature
r= cooling rate
I have the equation 95= (205 - 68)e^-.03t +68
I am just confused on how to solve for t and using logarithm/ natural long and the process for how to find t, etc. Thanks!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
T= (T0 - TR)e^-rt + TR
T= cooling time in minutes
T0= initial temperature
TR= room temperature
r= cooling rate
given:
+95+=+%28+205++-+68+%29%2Ae%5E%28-.03t%29+%2B+68+
+%28+205+-+68+%29%2Ae%5E%28+-.03t+%29+=+95+-+68+
+137%2Ae%2A%28+-.03t+%29+=+27+
+e%5E%28+-.03t+%29+=+27%2F137+
+e%5E%28+-.03t+%29+=+.19708+
Take the natural log of both sides
+-.03t+=+ln%28+.19708+%29+
+-.03t+=+-1.6241+
+t+=+54.1382+
+.1382%2A60+=+8.29+
The time is 54 min 8 sec
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If you have trouble with +ln%28+e%5E%28-.03t+%29%29+, say it in words
and it becomes clearer:
What is the log to the base e that gives me as a result
+e%5E%28+-.03t+%29+ ? It must be +-.03t+.
Does this help?