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A body was found in a room when the room's temperature was 66°F. Let f(t) denote the temperature of the body, t hours from the time of death. According to Newton's law of cooling, f satisfies a differential equation of the form y' = k(T-y). Answer parts (a) - (d) below. (a) Find T. T= 66 ° F (b) After several measurements of the body's temperature, it was determined that when the temperature of the body was 79 degrees, it was decreasing at a rate of 5 degrees per hour. Find k. k= .385 (Round to three decimal places as needed.) (c) Suppose that at the time of death, the body's temperature was about normal, say 98°F. Determine f(t). f(t) = 32 e - 385t, (Use integers or decimals for any numbers in the expression.) + 66 (d) When the body was discovered, its temperature was 86°F. Determine how long ago the person died. The person died hours before discovery. (Do not round until the final answer. Then round to three decimal places needed.)

A body was found in a room when the room's temperature was 66°F. Let f(t) denote the temperature of the body, t hours from the time of death. According to Newton's law of cooling, f satisfies a differential equation of the form y' = k(T-y). Answer parts (a) - (d) below. (a) Find T. T= 66 ° F (b) After several measurements of the body's temperature, it was determined that when the temperature of the body was 79 degrees, it was decreasing at a rate of 5 degrees per hour. Find k. k= .385 (Round to three decimal places as needed.) (c) Suppose that at the time of death, the body's temperature was about normal, say 98°F. Determine f(t). f(t) = 32 e - 385t, (Use integers or decimals for any numbers in the expression.) + 66 (d) When the body was discovered, its temperature was 86°F. Determine how long ago the person died. The person died hours before discovery. (Do not round until the final answer. Then round to three decimal places needed.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A body was found in a room when the room's temperature was 66°F. Let f(t) denote the temperature of the body, t hours from the time of death. According to Newton's law of cooling, f satisfies a differential equation of the form y' = k(T - y). Answer parts (a) - (d) below. (a) Find T. T= 66 ° F (b) After several measurements of the body's temperature, it was determined that when the temperature of the body was 79 degrees, it was decreasing at a rate of 5 degrees per hour. Find k. k= .385 (Round to three decimal places as needed.) (c) Suppose that at the time of death, the body's temperature was about normal, say 98°F. Determine f(t). -.385t f(t) = 32 e + 66 (Use integers or decimals for any numbers in the expression.) (d) When the body was discovered, its temperature was 86°F. Determine how long ago the person died. The person died hours before discovery. (Do not round until the final answer. Then round to three decimal places as needed.)
Transcribed Image Text:A body was found in a room when the room's temperature was 66°F. Let f(t) denote the temperature of the body, t hours from the time of death. According to Newton's law of cooling, f satisfies a differential equation of the form y' = k(T - y). Answer parts (a) - (d) below. (a) Find T. T= 66 ° F (b) After several measurements of the body's temperature, it was determined that when the temperature of the body was 79 degrees, it was decreasing at a rate of 5 degrees per hour. Find k. k= .385 (Round to three decimal places as needed.) (c) Suppose that at the time of death, the body's temperature was about normal, say 98°F. Determine f(t). -.385t f(t) = 32 e + 66 (Use integers or decimals for any numbers in the expression.) (d) When the body was discovered, its temperature was 86°F. Determine how long ago the person died. The person died hours before discovery. (Do not round until the final answer. Then round to three decimal places as needed.)
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