Question

A thermometer is removed from a room where the temperature is 70 F and is taken outside where the air temperature is 10 F. After one half minute the thermometer reds 50 F. what i the reading of the thermometer at t=1min? how long will it take for the thermometer to reach 15 F

Answer 1

I just need to be sure the givens are correct

in other words,

\[T_m=10 F\]
\[T(0)=70F\]

does time have to be in a certain measurement : hours, minutes, seconds?

Answer 2

looks like newton's law of cooling? use the same time units the problem uses... minutes.

Answer 3

so T(.5)=50

T(1)=?

Answer 4

\[\frac{dT}{dt}=k(T-10)\]

Answer 5

\[\frac{dT}{T-10}=kdt\]

Answer 6

ln(T-10)=kt+c

\[T-10=ce^{kt}\]

\[T=10+ce^{kt}\]

Answer 7

70=10+c

c=60

\[T=10+60e^{kt}\]

Answer 8

\[50=10+60e^{.5k}\]

\[40=60e^{.5k}\]
\[\frac{40}{60}=e^{.5k}\]
\[ln(\frac{1}{3})=.5k\]

\[\frac{-ln(3)}{.5}=k\]

Answer 9

\[T=10+60e^{-2.2}\]

Answer 10

2/3's wups

Answer 11

yay error fixed