1. Estimating the Temperature of a Yam You put a yam in a hot oven, maintained at a constant temperature of 200°C. As the yam picks up heat from the oven, its temperature rises. (a) Draw a possible graph of the temperature T of the yam against time t (minutes) since it is put into the oven. Explain any interesting features of the graph, and in particular explain its concavity. (b) At t = 30, the temperature T of the yam is 120° and increasing at the (instantaneous) rate of 2°/min. Using this information and the shape of the graph, estimate the temperature at time t = 40. (c) In addition, you are told that at t = 60, the temperature of the yam is 165°. Can you improve your estimate of the temperature at t = 40? (d) Assuming all the data given so far, estimate the time at which the temperature of the yam is 150°.
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- The yam is placed in an oven at a constant temperature of 200°C. - At \( t = 30 \) minutes, the temperature \( T \) of the yam is 120°C and increasing at a rate of 2% per minute. - At \( t = 60 \) minutes, the temperature \( T \) of the yam is 165°C. Show more…
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The following graph describes the temperature $T(t)$ of a yam in an oven, where temperature $T$ is measured in degrees Fahrenheit and time $t$ is measured in minutes: (a) Use the graph to approximate the temperature of the yam when it is first put in the oven. (b) Use the graph to approximate $\lim _{t \rightarrow \infty} T(t)$. (c) What is the temperature of the oven, and why?
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A yam is put in a hot oven, maintained at a constant temperature of 200 degrees C. At time t=30 minutes, the temperature T of the yam is 120 degrees and is increasing at an (instantaneous) rate of 2 degrees/min. Newton's law of cooling (or, in our case, warming) implies that the temperature at time t is given by T(t) = 200 - ae^(-bt). Find a and b.
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