# math

posted by
**Anonymous**
.

1. Estimating the Temperature of a Yam

Suppose you put a yam in a hot oven, maintained at a constant temperature of 200C. 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