Barbara1993
New member
- Joined
- Aug 27, 2014
- Messages
- 5
1.Suppose you put a yam in a hot oven, maintained at a constant temperature of 200C. As
(a) newton's law of heating and cooling states that the rate at which the temperature of the yam changes is proportional to the difference between its temperature and the temperature of the oven. Let H be the temperature of the yam after t minutes.Draw a possible graph of H vs time t (minutes). Explain any interesting features of the graph,(concavity).
(b) at t = 30, the temperature of the yam H=119.7and increasing at the (instantaneous)
rate of 2/min. Use the tangent line at t=30 to approximate the temperature at time t = 40. Do you expect he estimate to be too low or too high? Why?
(c) at t = 50, the temperature of the yam H=151.3.Use the secant line between the point where t=30 and 50 to give a new approximation of the temperature at t=40 . Do you expect this estimate to be to high or too low ? Why ?
i started working on this using dT/dt=K (200-H(t))
using dT/dt= 2
After 30 min H(t)= 119.7 + 2t at t=0 H(0) = 119.7
i solve for the Constance K in my first equation
2= k(200-H(0))
help am I in the right track?
(a) newton's law of heating and cooling states that the rate at which the temperature of the yam changes is proportional to the difference between its temperature and the temperature of the oven. Let H be the temperature of the yam after t minutes.Draw a possible graph of H vs time t (minutes). Explain any interesting features of the graph,(concavity).
(b) at t = 30, the temperature of the yam H=119.7and increasing at the (instantaneous)
rate of 2/min. Use the tangent line at t=30 to approximate the temperature at time t = 40. Do you expect he estimate to be too low or too high? Why?
(c) at t = 50, the temperature of the yam H=151.3.Use the secant line between the point where t=30 and 50 to give a new approximation of the temperature at t=40 . Do you expect this estimate to be to high or too low ? Why ?
i started working on this using dT/dt=K (200-H(t))
using dT/dt= 2
After 30 min H(t)= 119.7 + 2t at t=0 H(0) = 119.7
i solve for the Constance K in my first equation
2= k(200-H(0))
help am I in the right track?
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