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(Solved): The temperature is changing over the course of a day from 8 AM to 8 PM according to T^(')(t)=-0.06t^ ...
The temperature is changing over the course of a day from 8 AM to 8 PM according
to
T^(')(t)=-0.06t^(2)+0.4t+0.7
\deg (F)/() hour where t=0 corresponds to 8 AM . Using this function, answer the following
questions.
(a) Find T(t), the general solution to the problem. Use C as the constant of integra-
tion.
(b) If the temperature at when t=1 is 25\deg F, find C.
(c) Write out T(t), the particular solution and determine what the temperature is at
3 PM. Write your answer in a sentence in the context of the problem.