Applications of Exponential & Log Function Derivatives
6. A casting is taken from one oven at 1500F and placed into another at 0F, but rising at a rate of 100o/hr. The temperature is then:
T = 100t + 1500
Find the minimum temperature and when it occurs.
You know the steps: Take the derivative with respect to time, zero it equal to zero, and solve.
dT/dt = 100 + 1500(-0.2)e-0.2t
0 = 100 – 300e-0.2t
100 = 300e-0.2t
1/3 = e-0.2t
ln(1/3) = -.2t
t = 5.49 hr
The minimum temperature that corresponds to this is:
T = 100(5.49) + 1500e-0.2(5.49) = 1049o