A roast is taken from the refrigerator, where the temperature is [tex]40^\circ F[/tex], and put in a [tex]350^\circ F[/tex] oven. One hour later, the meat thermometer shows a temperature of [tex]90^\circ F[/tex]. If the roast is done when its temperature reaches [tex]155^\circ F[/tex], what is the total time the roast should be in the oven? Use Newton's Law of Cooling, which states that the rate of change of temperature is proportional to the difference between the temperature of the object and the temperature of the surrounding air. Round your answer to 2 decimal places.

[tex]t =[/tex] hours.

The roast should be in the oven for approximately 2.36 hours to reach a temperature of 155∘F. This calculation is based on Newton's Law of Cooling, which states that the rate of change of temperature is proportional to the difference between the object's temperature and the surrounding air temperature.

Newton's Law of Cooling can be expressed as:

dT/dt = -k(T - Ta)

where dT/dt is the rate of change of temperature, k is the proportionality constant, T is the temperature of the object, and Ta is the temperature of the surrounding air.

To find the total time the roast should be in the oven, we need to solve the differential equation above. By rearranging the equation and integrating, we can find the time it takes for the roast to reach a temperature of 155∘F.

The solution to the differential equation is:

T(t) = Ta + (To - Ta)e^(-kt)

where To is the initial temperature of the roast.

By plugging in the given temperatures and solving for t, we find that the roast should be in the oven for approximately 2.36 hours.

Learn more about temperature here: brainly.com/question/28884653

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