Answer:
Tt = Ts + Ce^-kt
Tt = 62 + 138e^-0.0068t
Step-by-step explanation:
The initial value problem for the Newton cooling rate is :
Tt = Ts + Ce^-kt
Initial temperature,when freshly poured Ti = 200°F
Temperature after 11 minutes = 190°F
Temperature of room, Ts= 62°F
Using the relation :
Tt = Ts + Ce^-kt
Temperature after time, t
When freshly poured, t = 0
k = constant of proportionality
We can then solve for C and k as follows :
200 = 62 + Ce^-0k
200 = 62 + C
C = 200 - 62 = 138°F
Using the Temperature after 11 minutes ; we can find, k, proportionality constant:
Temperature, Tt after, t = 11 minutes = 190
Tt = Ts + Ce^-kt
190 = 62 + 138e^-11k
128 = 138e^-11k
128 / 138 = e^-11k
0.9275 = e^-11k
Take In of both sides :
−0.075223 = - 11k
k = −0.075223 / - 11
k = 0.0068
The model function becomes :
Ts = 62 ; C = 138
Tt = 62 + 138e^-0.0068t
