Question 81608: A person buys a cup of coffee and drinks it in the store. The temp of the coffee y (in F degrees) is given by y=70 +137e to the power of -0.06t. t=time in minutes.a:What is the temp of the coffee when the person bought it? b:If the person will begin drinking the coffee when it reaches 180 degrees how much time must he wait after buying it? Thanks so much I am pulling my hair out
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A person buys a cup of coffee and drinks it in the store. The temp of the coffee y (in F degrees) is given by y=70 +137e to the power of -0.06t. t=time in minutes.a:What is the temp of the coffee when the person bought it? b:If the person will begin drinking the coffee when it reaches 180 degrees how much time must he wait after buying it?
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f(x) = 70 + 137e^(-0.06t)
When the person bought the coffee the time was zero.
So, f(0)=70+137^(-0.06*0) = 70 + 137 = 207 degrees
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If the coffee is at 180 degrees the equation becomes:
180=70+137e^(-0.06t)
110 = 137e^(-0.06t)
e^(-0,06t)= 0.802919708
Take the natural log to get:
-0.06t = -0.21950056
t=3.658 minutes
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Cheers,
Staan H.
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