SOLUTION: Newton's law of cooling relates the rate at which a body cools to the difference in temperature between the body and the environment into which it is introduced. The formula is F(t

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Question 947630: Newton's law of cooling relates the rate at which a body cools to the difference in temperature between the body and the environment into which it is introduced. The formula is F(t) = To + Cb^t, where F(t) is the temperature of the body at time t, To is the constant temperature of the environment into which the body is introduced, and C and b are constants. Use Newton's law of cooling to solve the problem below.
A cup of coffee has cooled from 96° to 50° after 10 minutes in a room at 22°. How long will it take to cool to 40°?

Please note: o is suppose to be a subscript

Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Form two equations based on the formula.

system%2822%2BC%2Ab%5E0=96%2C22%2BC%2Ab%5E10=50%29

system%28Cb%5E0=74%2CC%2Ab%5E10=28%29

Some simplification more

C%2A1=74
highlight%28C=74%29
and
highlight%28C%2Ab%5E10=28%29

C now known, and b is easily found.