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)=T_a+(T₀-T_a)e^-kt. In this model, T_a 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 131F. The water heater is shut off and the water cools to the temperature of the surrounding air, which is 80F. 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 116F. 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?

Select one:

a. No; the temperature after 24 hr will be approximately 80F

b. Yes; the temperature after 24 hr will be approximately 127F

c. No; the temperature after 24 hr will be approximately 106F

d. Yes; the temperature after 24 hr will be approximately 128F