Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. suppose that the temperature of a cup of coffee obeys newton's law of cooling. if the coffee has a temperature of 190 degrees fahrenheit when freshly poured, and 2 minutes later has cooled to 170 degrees in a room at 66 degrees, determine when the coffee reaches a temperature of 145 degrees.

t=5.18 minute

Step-by-step explanation:

Using Newton's law of cooling

T is temperature of a cup of coffee at any time t , is the temperature of the surrounding and k is a constant of proportionality in this negative because temperature is decreasing.

To find constant knowing the time and the temperature the first step of the change of energy in cup of coffee

Now using the constant of decreasing can find the time to be a 145 temperature the cup of coffee

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