A coroner arrives on the scene of a homicide at 10:00 p.m. in a temperature-controlled room, held at 70 degrees F. The temperature, y, in degrees Fahrenheit, of the victim is given by the function y=f(t)=22.4e^{(-0.19t)}+70, where t is time in hours after 10:00 p.m.
A) What is the practical range of this function? What values of y make sense in this scenario? What's the warmest this body could have been? What is the coldest it can get in the room?
B) What is the y-intercept of the function? Explain what this means in a sentence including the clock time.
C) Based on the graph of the function, what time t corresponds to a normal human temperature of 98.6 degrees? Round your answer to the nearest hundredth (2 decimal places). What does this value of t represent in the context of the scenario? D) A neighbor tells the detective she and the victim were having drinks at 9:15. Does this story make sense?