anonymous
  • anonymous
The temperature of a body is measured as 104oF. It is observed that the amount the temperature changes for each period of two hours is -0.3 time the difference between the previous period's temperature and the room temperature, which is 70oF. a. Write a recurrence relation for tn, the temperature of the body at the end of n 2-hour time periods. b. Find a general and particular solution for the system and give the value of t(12), the temperature of the body after 24 hours. c. Does this system have an equilibrium value? If so, what is it?
Mathematics
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anonymous
  • anonymous
The temperature of a body is measured as 104oF. It is observed that the amount the temperature changes for each period of two hours is -0.3 time the difference between the previous period's temperature and the room temperature, which is 70oF. a. Write a recurrence relation for tn, the temperature of the body at the end of n 2-hour time periods. b. Find a general and particular solution for the system and give the value of t(12), the temperature of the body after 24 hours. c. Does this system have an equilibrium value? If so, what is it?
Mathematics
chestercat
  • chestercat
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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dumbcow
  • dumbcow
Tn = Tn-1 - 0.3(Tn-1 - 70) Tn = 0.7Tn-1 + 21 t(n) = 34(.7)^n + 70 t(12) = 70.47

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