A cup of coffee is placed in a room maintaining a constant temperature of 81°F at time t = 0. The temperature of the coffee after t minutes in the room is described by the function
Based on this model, how long does it take the coffee to cool to a temperature of 92°F?

Question

anonymous · Answer

wts the function?

anonymous · Answer

attachment

bahrom7893 · Answer

This is easy just plug in 92 instead of C(t) and solve for t

anonymous · Answer

56.89 minutes

anonymous · Answer

yeah

bahrom7893 · Answer

92 = 81+101e^(-0.039t)
92-81 = 101e^(-0.039t)
11 = 101e^(-0.039t)
11/101 = e^(-0.039t)
0.1089 = e^(-0.039t)
take ln on both sides..

bahrom7893 · Answer

Ln0.1089 = lne^(-0.039t)
Ln0.1089 = (-0.039t)*Lne ( Ln(a^b) = b*Ln(a), memorize this )
Ln0.1089 = (-0.039t)*1   ( Ln(e)=1, memorize this )
Ln0.1089 = (-0.039t)
t = Ln0.1089 / -0.039

bahrom7893 · Answer

t = 56.85449 according to wolframalpha and yea so roughly 57 hours and hero is right

anonymous · Answer

Isn't that in minutes?

bahrom7893 · Answer

oh yea i think so.. about an hour haha

bahrom7893 · Answer

*roughly 57 minutes not hours..