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1. The temperature of a body is measured as 110° F. It is observed that the amount the temperature changes during each period of two hours is -0.3 times the difference between the previous periods temperature and the room temperature, (ie 70° F). (a) Write a difference equation that describes the temperature T(n) of the body at the end of n periods. (b) Find T(n).

1. The temperature of a body is measured as 110° F. It is observed that the amount the temperature changes during each period of two hours is -0.3 times the difference between the previous periods temperature and the room temperature, (ie 70° F). (a) Write a difference equation that describes the temperature T(n) of the body at the end of n periods. (b) Find T(n).

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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1. The temperature of a body is measured as 110° F. It is observed that the amount the temperature changes during each period of two hours is -0.3 times the difference between the previous periods temperature and the room temperature, (ie 70 F). (a) Write a difference equation that describes the temperature T (n) of the body at the end of n periods. (b) Find T(n). 2. The proportion of carbon-14 in plants and animals is the same as that in the atmo- sphere as long as the plant or the animal is alive. When an animal or plant dies, the carbon-14 in its tissue starts decaying at the rate r. (a) If the half-life of carbon-14 is 5,700 years, find r. (b) If the amount of carbon-14 present in a bone of an animal is 70% of the origi- nal amount of carbon-14, how old is the bone?
Transcribed Image Text:1. The temperature of a body is measured as 110° F. It is observed that the amount the temperature changes during each period of two hours is -0.3 times the difference between the previous periods temperature and the room temperature, (ie 70 F). (a) Write a difference equation that describes the temperature T (n) of the body at the end of n periods. (b) Find T(n). 2. The proportion of carbon-14 in plants and animals is the same as that in the atmo- sphere as long as the plant or the animal is alive. When an animal or plant dies, the carbon-14 in its tissue starts decaying at the rate r. (a) If the half-life of carbon-14 is 5,700 years, find r. (b) If the amount of carbon-14 present in a bone of an animal is 70% of the origi- nal amount of carbon-14, how old is the bone?
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