How do I form an exponential function with a set of data

Question

I'm working on a project to do with exponential function and I'm trying to extrapolate a set of data to find the variables needed for the analysis of the experiment (the goal of which is to compare the speed boiled tap water and salt water reach to room temperature). Using the form Ab^x+C I tried extrapolating on desmos but the horizontal asymptote was higher than room temperature. I tried changing the C but it changed the y intercept, so how can I form an exponential function based on a set of data?

Answer 1

If you are assuming Newton's law of cooling, the temperature of the water should be

θ = (T-T_amb)/(T₀-T_amb) = e^-Ut/(mC) where U is a heat transfer coefficient (J/K-s) (The nondimensional Temperature on the LHS of the equation will vary from 1 to 0.) A is surface area of the pot, m is mass if the solution, C is the specific heat.

In order for this function to form a line you need to plot lnT or ln(θ) vs. t

lnθ = -(U/mc) t

(You can do the same thing for lnT in order to interpret slope and intercept.)

ln(T-T_amb) = ln(T₀-T_amb) -(U/mc)t

Please consider a tutor. Take care.

Answer 2

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