Solution Found!
A cup of coffee cools according to Newton’s law of cooling
Chapter 1, Problem 5E(choose chapter or problem)
A cup of coffee cools according to Newton’s law of cooling (3). Use data from the graph of the temperature T(t) in Figure 1.3.10 to estimate the constants \(T_{m}\), \(T_{0}\), and k in a model of the form of a first-order initial-value problem: \(d T / d t=k\left(T-T_{m}\right)\), \(T(0)=T_{0}\).
Text Transcription:
T_m
T_0
dT/dt = k(T-T_m)
T(0)=T_0
Questions & Answers
QUESTION:
A cup of coffee cools according to Newton’s law of cooling (3). Use data from the graph of the temperature T(t) in Figure 1.3.10 to estimate the constants \(T_{m}\), \(T_{0}\), and k in a model of the form of a first-order initial-value problem: \(d T / d t=k\left(T-T_{m}\right)\), \(T(0)=T_{0}\).
Text Transcription:
T_m
T_0
dT/dt = k(T-T_m)
T(0)=T_0
ANSWER:Step 1 of 3
In this problem we have to find the value of using the graph.
Where is the temperature at
.
Therefore we can read it from the graph,
It shows to be
Hence