A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 79°C, it is cooling at a rate of 1°C per minute. When does this occur? (Round your answer to two decimal places.)

Question

anonymous · Answer

This is a rate of change problem, so you are going to need calculus - we need some assumptions here - as to the type of relationship. At the moment, you know dT/dt at a particular time, and To

anonymous · Answer

Wouldn't it be something along the lines of dT/dt = 20+95e^kt?

anonymous · Answer

Then we would go ahead and substitute for k, giving us T(79) = 20+95e^(1)k?

anonymous · Answer

I mean 20+95e^1t, substituting for k

anonymous · Answer

ok, so you are modelling temp using the exponential function, and k will be negative.
Let T=20+75e^(kt) so when t=0, T=95 (since 20 +75=95).
When T=79 we have 
79=20+75e^(kt)    (1)
and differentiating to get
dT/dt=k*75e^(kt)=-1   (2)
So We have two equations,  rearrange (1) to get what e^kt equals substitute it into the second to solve for k, then you can solve for t using either (1) or (2) and ln

anonymous · Answer

You can solve this now?