Exponential and Logarithmic Models

Question

An object with initial temperature  is submerged in large tank of water whose temperature is .

Find a formula for , the temperature of the object after  minutes, if the cooling constant is 

=

Answer 1

F(t)=Ae^kt+F_a

At t=0 F(t)=200°F so you can solve for A:

F(0)=Ae^kt+F_a

200=Ae^0.2(0)+50

150=A(1)

150=A

Now, we know A so we can plug into the equation:

F(t)=Ae^kt+50

F(t)=150e^0.2t+50