Section
2.3
Modeling
with
First
Order:
Problem
8
(1
point)
A
thermometer
is
taken
from
a
room
where
the
temperature
is
22°C
to
the
outdoors,
where
the
temperature
is
—10°C.
After
one
minute
the
thermometer
reads
12°C.
(@)
What
will
the
reading
on
the
thermometer
be
after
3
more
minutes?
n
will
the
thermometer
read
—9°C?
minutes
after
it
was
taken
to
the
outdoors.
Solution:
Let
T'(#)
be
the
temperature
at
time
¢,
measured
in
minutes.
T(1)
satisfies
the
differential
equation
dT
—
=—k(T+1
&
(T
+
10)
with
solution
T(t)
=10+
Ce™™
Since
T'(0)
=
22,
we
have
T(t)
=
—10
+
32¢7
After
one
minute
the
temperature
is
12,
thus
12
=
=10+
32¢7%,
which
gives
k
=
—
ln(%)
=~
0.374693.
Hence
T(f)
=
—10
+
3270374693
(a)
The
reading
on
the
thermometer
after
3
more
minutes
will
be
T(4)
=
—10
+
32¢7037465®
~ 2
85106
(a)
To
find
when
the
termomether
will
read
—9,
we
solve
the
equation
0
=
—10
4
3270374693
This
gives
t
=
9.24953
minutes.
