Newtons law of cooling

Question

A yam which is initially at 45 degrees F is placed in an oven which is at 425 degrees F. The rate of change is known to be -.19, when t is measured in hours. How long to the nearest minute will it take for the yam to reach a temperature of 145 degrees F. 

Recall Newtons law of cooling T(t)=C+(T  - C) e^kt

                                                          0

Answer 1

T(t) = Ta + (T0 - Ta)*e^(-kt)

 

T0 = 45 deg

 

Ta = 425 deg

 

k = 0.19

 

T(t1) = 145 deg with t1 = hours it took for T to go from T0 to T(t1)

 

T(t1) = Ta + (T0 - Ta)*e^(-k t1)

 

145 = 425 + (45 - 425)*e^-(0.19 t1)

 

-280 = -380e^-(0.19 t1)

 

t1 = -(1/0.19)*ln(280/380) = 1.60727 hrs = 96.436 min = 1 hr + 36.436 min