# algebra

A cup of coffee is heated to 180°F and placed in a room that maintains a temperature of 65°F. The temperature of the coffee after t minutes is given by T(t) = 65 + 115e^−0.042t.(a) Find the temperature, to the nearest degree, of the coffee 10 minutes after it is placed in the room.
_ °F ?

(b) Use a graphing utility to determine when, to the nearest tenth of a minute, the temperature of the coffee will reach 110°F.
After ? min

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1. let's just plug in t = 10

T(10) = 65 + 115 e^-.42
= 140.56
= 141° to the nearest degree.

b)
we want 110 = 65 + 115 e^(-.042t)
e^(-.042t) = (110-65)/115 = .391304...
take ln of both sides
-.042t = ln .391304..
t = 22.34 minutes or 22.3 minutes

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