# math

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1. Estimating the Temperature of a Yam
Suppose 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.16
(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) Suppose that, at t = 30, the temperature T of the yam is 120 and increasing at the (instantaneous)
rate of 2/min. Using this information, plus what you know about the shape of the
T graph, estimate the temperature at time t = 40.
(c) Suppose 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

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