SOLUTION: This exercise uses Newton's Law of Cooling. A hot bowl of soup is served at a dinner party. It starts to cool according to Newton's Law of Cooling so that its temperature at tim

Algebra ->  Trigonometry-basics -> SOLUTION: This exercise uses Newton's Law of Cooling. A hot bowl of soup is served at a dinner party. It starts to cool according to Newton's Law of Cooling so that its temperature at tim      Log On


   

Question 979493: This exercise uses Newton's Law of Cooling.
A hot bowl of soup is served at a dinner party. It starts to cool according to Newton's Law of Cooling so that its temperature at time t is given by
T(t) = 67 + 148e−0.05t
where t is measured in minutes and T is measured in °F.
(a) What is the initial temperature of the soup?=?f
whats is the temperature after 10 minutes?
c. How long will it be until its 100 F
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Initially, t=0
T%280%29=67%2B148e%5E0
T%280%29=67%2B148
T%280%29=215
.
.
T%2810%29=67%2B148e%5E%28-0.5%29
T%2810%29=67%2B89.8
T%2810%29=156.8
.
.
100=67%2B148e%5E%28-0.05t%29
148e%5E%28-0.05t%29=33
e%5E%28-0.05t%29=0.22297
-0.05t=ln%280.22297%29
t=-20%2Aln%280.22297%29