Newton’s Law of Cooling (See the textbook for the formula) is used to determine time of death in homicide investigations. Assuming a normal body temperature of 98.6! F , and that time since death is measured in hours, the constant in Newton’s Law of Cooling is given to be k = 0.1947. Suppose the temperature of the room is 58! F : Find a function F (t ) , which models the body’s temperature t hours after death. Use EXACT V ALUES. If the temperature of the body at 8 PM was 62! F , what time did the person die? Please give the exact answer and a decimal approximation correct to 2 decimal places.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Newton’s Law of Cooling (See the textbook for the formula) is used to determine time of death in homicide investigations. Assuming a normal body temperature of 98.6! F , and that time since death is measured in hours, the constant in Newton’s Law of Cooling is given to be k = 0.1947. Suppose the temperature of the room is
58! F :
-
Find a function F (t ) , which models the body’s temperature t hours after death. Use EXACT
V ALUES.
-
If the temperature of the body at 8 PM was 62! F , what time did the person die? Please give the exact answer and a decimal approximation correct to 2 decimal places.
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