According to Newton's law of cooling, the temperature T of a body at time t is given by T = Ta + (T0 − Ta)e−kt , where Ta is the ambient temperature, T0 is the initial temperature, and k is the cooling rate constant. For a certain type of beverage container, the value of k is known to be 0.025 min−1.
a. Assume that Ta = 36oF exactly and that T0 = 72.0 ± 0.5oF. Estimate the temperature T at time t = 10 min, and find the uncertainty in the estimate.
b. Assume that T0 = 72oF exactly and that Ta = 36.0 ± 0.5oF. Estimate the temperature T at time t = 10 min, and find the uncertainty in the estimate.