Solve the problem.
Newton's law of cooling indicates that the temperature of a warm object will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature T(t) is modeled by T(t) = Ta + (T0 - Ta)e-kt. In this model, Ta represents the temperature of the surrounding air, T0 represents the initial temperature of the object and t is the time after the object starts cooling. The value of k is the cooling rate and is a constant related to the physical properties of the object.
Water in a water heater is originally 131°F. The water heater is shut off and the water cools to the temperature of the surrounding air, which is 80°F. The water cools slowly because of the insulation inside the heater, and the rate of cooling is 0.00348. Dominic does not like to shower with water less than 116°F. If Dominic waits 24 hr after the heater is shut off, will the water still be warm enough for a shower? How warm will the water be?
a. No; the temperature after 24 hr will be approximately 80°F
b. Yes; the temperature after 24 hr will be approximately 127°F
c. No; the temperature after 24 hr will be approximately 106°F
d. Yes; the temperature after 24 hr will be approximately 128°F
b. Yes; the temperature after... View the full answer