More Exp. Growth and Decay help needed!! (1 Viewer)

[NizDiz]

How do u even... do question 4??? Completely lost

 

[omgiloverice]

weird question o.o what is the answer?

 

[braintic]

How do u even... do question 4??? Completely lost

Without cooling, dT/dt = +5
Without heating, dT/dt = -k(T-20)

Combining heating and cooling: dT/dt = 5 - k(T-20)

We need dT/dt to approach zero as T approaches 120 degrees.
5 - k(T-20) = 120
k=0.05

dT/dt = 5 - 0.05(T-20)
= 6 - 0.05T
= -0.05 (T-120)

This is standard differential form for Newton Cooling.
So T = 120 + Be^(-0.05t)
(t=0, T=20) 20 = 120 + B
B=-100

So T = 120 - 100e^(-0.05t)

Substitute T = 100 and solve to get answer t = 32.2 minutes