SOLUTION: A cup of tea cools exponentially according to the function T(x)=60(0.79)(^x/3)+30,where T is the temperature in degrees celcius and x is time in minutes. What was the initial tempe

Algebra ->  Exponents -> SOLUTION: A cup of tea cools exponentially according to the function T(x)=60(0.79)(^x/3)+30,where T is the temperature in degrees celcius and x is time in minutes. What was the initial tempe      Log On


   

Question 126690: A cup of tea cools exponentially according to the function T(x)=60(0.79)(^x/3)+30,where T is the temperature in degrees celcius and x is time in minutes. What was the initial temperature of the tea? I think it is 90 degrees celcius. Can someone kindly confirm ???
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A cup of tea cools exponentially according to the function T(x)=60(0.79)^(x/3)+30,where T is the temperature in degrees celcius and x is time in minutes. What was the initial temperature of the tea? I think it is 90 degrees celcius. Can someone kindly confirm ???
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The "initial time" means x=0
If x=0 in your formula, T(0) = 60
That is the initial temperature.
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The initial temperature occurs when t=0


T%28x%29=60%280.79%29%5E%28t%2F3%29%2B30 Start with the given equation



T%280%29=60%280.79%29%5E%280%2F3%29%2B30 Plug in t=0


T%280%29=60%280.79%29%5E0%2B30 Reduce the exponent 0%2F3 to 0


T%280%29=60%281%29%2B30 Raise 0.79 to the zeroth power to get 1


T%280%29=60%2B30 Multiply


T%280%29=90 Add



So the initial temperature is 90 degrees. So you are correct.