Need help with Newton's Law of Cooling math problem

In summary, Newton's Law of Cooling is a mathematical equation that describes the rate at which an object cools down or heats up when exposed to a different temperature. The formula for this law is T(t) = T<sub>s</sub> + (T<sub>0</sub> - T<sub>s</sub>)e<sup>-kt</sup>, where T(t) is the temperature of the object at time t, T<sub>s</sub> is the surrounding temperature, T<sub>0</sub> is the initial temperature of the object, and k is a constant determined by the specific properties of the object and its surroundings. The units of measurement for the variables in this formula are degrees Celsius (
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A detective finds a murder victim at 9 AM. The temperature of the body is measured at 90.3-degrees Fahrenheit. One hour later the temperature of the body is 89.0-degrees Fahrenheit. The temperature of the room has been maintained at a constant temperature of 68-degrees Fahrenheit. Estimate the time the murder occurs. I went through the problem and got a time of .229 hours but I'm not sure that number makes sense since shouldn't I be getting a negative number? Please help! Thank you.
 
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Nvm everyone. I was able to find my error!
 

What is Newton's Law of Cooling?

Newton's Law of Cooling is a mathematical equation that describes the rate at which an object cools down or heats up when exposed to a different temperature.

What is the formula for Newton's Law of Cooling?

The formula for Newton's Law of Cooling is T(t) = Ts + (T0 - Ts)e-kt, where T(t) is the temperature of the object at time t, Ts is the surrounding temperature, T0 is the initial temperature of the object, and k is a constant determined by the specific properties of the object and its surroundings.

What are the units of measurement for the variables in the Newton's Law of Cooling formula?

The units of measurement for the variables in the formula are as follows: T(t) and Ts are in degrees Celsius (°C), T0 is in degrees Celsius (°C) or Kelvin (K), t is in seconds (s), and k is in inverse seconds (s-1).

Can Newton's Law of Cooling be applied to all cooling or heating scenarios?

No, Newton's Law of Cooling is only applicable to scenarios where the object is in thermal contact with its surroundings and the temperature difference is not too large.

How can I use Newton's Law of Cooling to solve a math problem?

To solve a math problem using Newton's Law of Cooling, you will need to gather all the necessary information (initial temperature, surrounding temperature, time, and k value) and plug them into the formula. Then, you can solve for the unknown variable using algebraic methods or a graphing calculator.

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