Hi, I would like some guidance with this intro differential equation 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 Tm, T0, and k in a model of the form of a rst-order initial-value problem: dT/dt = k(T − Tm), T(0) = T0 I understand that T0 = 180, and Tm = 75, and I understand to find K, I need to solve for it which leaves me with this equation: k=(dT/dt)/(T-Tm) Where I am getting lost is, how do I find the value of dT/dt, and the value of T. Thanks
Hi, I would like some guidance with this intro differential equation 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 Tm, T0, and k in a model of the form
of a rst-order initial-value problem: dT/dt = k(T − Tm),
T(0) = T0
I understand that T0 = 180, and Tm = 75, and I understand to find K, I need to solve for it which leaves me with this equation: k=(dT/dt)/(T-Tm)
Where I am getting lost is, how do I find the value of dT/dt, and the value of T.
Thanks
https://www.bartleby.com/solution-answer/chapter-13-problem-5e-differential-equations-with-boundary-value-problems-mindtap-course-list-9th-edition/9781337604918/a-cup-of-coffee-cools-according-to-newtons-law-of-cooling-3-use-data-from-the-graph-of-the/c55ea0ff-5726-43b3-a76d-bbb783ce7537
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