SOLUTION: A cup of coffee is heated to 180°F and placed in a room that maintains a temperature of 60°F. The temperature of the coffee after t minutes is given by T(t) = 60 + 115e−0.0

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Question 1130983: A cup of coffee is heated to 180°F and placed in a room that maintains a temperature of 60°F. The temperature of the coffee after t minutes is given by
T(t) = 60 + 115e−0.042t.
(a) Find the temperature, to the nearest degree, of the coffee 20 minutes after it is placed in the room._________°F
(b) Determine when, to the nearest tenth of a minute, the temperature of the coffee will reach 145°F.______________min
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A cup of coffee is heated to 180°F and placed in a room that maintains a temperature of 60°F. The temperature of the coffee after t minutes is given by
T%28t%29+=+60+%2B+115e%5E%28-0.042t%29.
:
(a) Find the temperature, to the nearest degree, of the coffee 20 minutes after it is placed in the room._________°F
T%28t%29+=+60+%2B+115e%5E%28-0.042%2A20%29
T%28t%29+=+60+%2B+115e%5E%28-.84%29
T(t) = 60 + 115(.4317)
T(t) = 60 + 49.6
T(t) = 109.6 degrees after 20 min
:
(b) Determine when, to the nearest tenth of a minute, the temperature of the coffee will reach 145°F.______________min
60+%2B+115e%5E%28-0.042t%29=+145
115e%5E%28-0.042t%29=+145+-+60
115e%5E%28-0.042t%29=+85
e%5E%28-0.042t%29=+85%2F115
e%5E%28-0.042t%29=+.739
using nat logs
-.042t*ln(e) = ln(.739)
ln(e) = 1, therefore
-.042t = -302
t = %28-301%29%2F%28-.042%29
t = +7.2 minutes it will be 145 degrees