A cup of coffee cools according to Newton's law of cooling (3) in Section 1.3. xT-Tm =k(T-Tm) (3) Use data from the graph of the temperature T(t) in the figure to estimate the constants Tm Tor and k in a model of the form of a first-order initial-value problem: dT/dt = k(T-Tm), T(0) = To- TA Tm= 200+ 150 100+ 50+ 0 25 50 75 100 minutes 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A cup of coffee cools according to Newton's law of cooling (3) in Section 1.3.
dT
K(T-Tm)
(3)
dt
Use data from the graph of the temperature T(t) in the figure to estimate the constants T
m'
To, and k in a model of the form of a first-order initial-value problem: dT/dt = k(T – Tm), T(0) = To·
m
=
k =
dT
dt
x T- Tm or
TA
200
150
100+
50+
0
=
+
25 50 75 100 t
minutes
Transcribed Image Text:A cup of coffee cools according to Newton's law of cooling (3) in Section 1.3. dT K(T-Tm) (3) dt Use data from the graph of the temperature T(t) in the figure to estimate the constants T m' To, and k in a model of the form of a first-order initial-value problem: dT/dt = k(T – Tm), T(0) = To· m = k = dT dt x T- Tm or TA 200 150 100+ 50+ 0 = + 25 50 75 100 t minutes
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