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a) At 2 PM a corpse is found with body temperature of 32° C. Ninety minutes later its temperature is 29° C. Assuming Newton's Law of Cooling applies, with an ambient temperature of 18° C, determine at what time (to the nearest minute) the person died.

a) At 2 PM a corpse is found with body temperature of 32° C. Ninety minutes later its temperature is 29° C. Assuming Newton's Law of Cooling applies, with an ambient temperature of 18° C, determine at what time (to the nearest minute) the person died.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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a) At 2 PM a corpse is found with body temperature of 32° C. Ninety minutes later its temperature is 29° C. Assuming Newton's Law of Cooling applies, with an ambient temperature of 18° C, determine at what time (to the nearest minute) the person died. b) A cylindrical tank has an inflow of fluid at 2 liters per minute, while there is a hole at the bottom where the fluid exits at a rate proportional to Vh, where h is the depth of the fluid. The tank initially contains 100 liters of fluid, 10 minutes later it has 108 liters. If the tank has a capacity of 150 liters, then when will the tank become full? c) The rate of change of the population in a certain region can be modeled by: dP Birth Rate) - (Death Rate), where the birth rate is dt proportional to the population and the death rate is proportional to the square root of the population. Give the DE that models this situation, then solve with the IC P(0) = Po.
Transcribed Image Text:a) At 2 PM a corpse is found with body temperature of 32° C. Ninety minutes later its temperature is 29° C. Assuming Newton's Law of Cooling applies, with an ambient temperature of 18° C, determine at what time (to the nearest minute) the person died. b) A cylindrical tank has an inflow of fluid at 2 liters per minute, while there is a hole at the bottom where the fluid exits at a rate proportional to Vh, where h is the depth of the fluid. The tank initially contains 100 liters of fluid, 10 minutes later it has 108 liters. If the tank has a capacity of 150 liters, then when will the tank become full? c) The rate of change of the population in a certain region can be modeled by: dP Birth Rate) - (Death Rate), where the birth rate is dt proportional to the population and the death rate is proportional to the square root of the population. Give the DE that models this situation, then solve with the IC P(0) = Po.
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