一.(a) A hungry college student, in a rush to eat, turns the oven on and puts
a frozen pizza in it, without preheating the oven. Let f(t) denote the
temperature of the pizza and T(t) the oven's temperature, t minutes after the
oven was turned on. According to Newton's law of cooling, the rate of change
of f(t) is proportional to the difference between the oven's temperature and
the temperature of the pizza. find a differential equation that is satisfied
by f(t).
(b) Suppose that the oven's temperature in (a) is given by T(t)= 70+50t for
0<=t<=8. Suppose further that the constant of proportionality is k=0.1 and
that the initial temperature of the frozen pizza was 27度 . Determine the
temperature of the pizza during the first 8minutes of heating.
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