Newton's Law for Heating and Cooling states that the temperature T of an object at time t is given by the formula

T left parenthesis t right parenthesis equals T subscript a plus open parentheses T subscript 0 minus T subscript a close parentheses times e to the power of negative k t end exponent

Where T subscript 0 is the initial temperature of the object.

T subscript a is the ambient temperature (i.e. the temperature of the surroundings), and

k greater than 0 is the constant of proportionality.



A 40 to the power of degree F roast is cooked in a 350 to the power of degree F oven. Assuming the the constant of proportionality k equals 0.1602 , 165 to the power of degree F and that the temperature of the roast follows Newton's Law. The roast is done when its internal temperature reaches 165 to the power of degree F . How long does the roast need to stay in the oven for it to be done? (You can assume that t is given in hours).


3.22


1.666


165 to the power of degree F


None of the above.