Question

a thermometer reading 18 F is brought into a room, the temperature of which is 70 F. one minute later the reading is 31 F. determine the temperature reading as a function of time. find the temperatire reading 5 minutes after the thermometer is first brought into the room

Answer 1

Given

T_m = 70 F

@ t = 0
T = 18

@ t = 1
T = 31

Answer 2

\[\ln (\frac{31 - 70}{18-70}) = k\]
\[\ln (0.75) = k\]
\[k = -0.2877\]

Answer 3

when t = 5 then

\[\ln (\frac{T - 70}{18 - 70} )= -0.2877(5)\]
\[\ln (\frac{T-70}{-52}) = -1.4385\]
\[T = 70 - 52e^{-1.4385}\]
\[T = 57.66 F\]

Answer 4

is that right?

Answer 5

yes

Answer 6

T as a function of time
\[\large T=70-52 e^{-1.4t}\]

Answer 7

okay thanks :D