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I have to use the program called Sage for my Differential Equations lab and I've never used it before. Can someone help? I measured the

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I have to use the program called Sage for my Differential Equations lab and I've never used it before. Can someone help?

I measured the temperature (in Fahrenheit) of a eup of tea at five different times, shown in the chart below imc Tcmp 10:30 175 10:33 163 10:371 152 10:42 142 10:52 127 In this lab you will use Newton's law of cooling. o explore modeling this data. As in class, denotes the lemperatue, is the ambient temperature, and is the time. I is simplest to let corespond to 10.30 am. Assume that te ambicnt tempcraturc was F A 70" 1. Use the first two data points and the solution to the differential cquation to calculate It may be helpful to do some of the algebra by hand. Plot the solution to the ODE with the data - does it look correet? 2. Use the last two data points to calculate. Again, plot the solution along with the datd Does i look beller or worse? 3. ee is always some er or in experimen al data when determining om the urst two dala points is lhe value of more senstve lo a 10% errori ostv e) n the lime or temperature ofuhe second data point? 4. Use the interactive cell below to find a good guess for Which data oint do you think has the largest crror in temierature? # for exercise 4 # it may be helpful to use portions of the code in this interactive cell # in the previous exercises as well var('t, T) interact def kft(k slider( .e1,.05, .001, default = "03), Te = slider(12e.e,185.1, .1, default = 175.0), to = slider(0,22, .1)); model_plot-plot (7e (Te-7) exp-(t-te)*k),0,22) data_plot- list_plot(I[e,175], [3,163], [7,152], [12,142], [22,127]], rgbcolor show(model_plot+data_plot) (1,e,0))

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