Question

# Murder Investigation: When a glass of wine with a certain temperature is placed into a room,...

Murder Investigation: When a glass of wine with a certain temperature is placed into a room, its temperature will converge to the room’s temperature according to the formula: F(t)=Fs+(F0-Fs) -.3t. Where F(t) is the temperature of the object after being in the room for t hours, F0 is the initial temperature of the object, and Fs is the temperature of the room that the object is in. Use this formula to investigate the scenario below and answer the following questions. Homicide Investigation #2424-1 Veronica Sly: wife of Samuel Sly allegedly comes home and finds her husband dead. 9:08 PM - She calls 911 When questioned by the 911 dispatcher, Mrs. Sly claimed that she came home at 9:00 PM, took a bottle of red wine from the cellar, poured a glass, and then found her husband dead in the bedroom. 9:22 PM – Authorities arrive on the scene. Mrs. Sly is immediately escorted to the police station for further questioning. 10:00 PM - CSI investigators measure several temperatures. Mrs. Sly’s half full glass of wine temperature was 65 degrees. The wine cellar has the wine bottles chilled at 45 degrees. The house thermostat is set at 72 degrees. Write the correct formula that models the temperature of the wine after being subjected to the room’s environment for t hours. Using increments of ½ hours for t, graph the formula below: What does the value of F(0) represent? If Mrs. Sly’s story is true, what should the wines temperature be at 10:00 pm? What temperature does F(t) converge to, as t gets very large? Using a graph, approximate how long it should take the wine’s temperature to rise to 65 degrees in this scenario. What time did the wife actually pour her glass of wine? At trial, Mrs. Sly’s lawyer claims the house thermostat was broken. For Mrs. Sly’s story to be true, what “real” home temperature does the lawyer need to claim? Would you believe this claim if you were one of the jurors?

i will not believe as room temperature is very high which is impossible

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