Exponential Function Regression

Question

I need to find the exponential function y = c0e^(c1*x) using fit in Mathematica for the data points {1850, 1.3}, {1900, 1.6}, {1950, 3.0}, {1980, 4.4}, {2000, 6.0}}.

Answer 1

Try this

data = {{1850, 1.3}, {1900, 1.6}, {1950, 3.0}, {1980, 4.4}, {2000, 6.0}};
f = a Exp[b (x/1850-x0)];
fit = FindFit[data, f, {a, b, x0}, x];
fit0 = f /. fit // Simplify
gr0 = ListPlot[data, PlotStyle -> Red];
gr1 = Plot[fit0, {x, 1850, 2000}];
Show[gr1, gr0]

so the adjust is

$$ y = 0.330376 e^{22.8667 \left(\frac{x}{1850}-0.955521\right)} $$

or also

$$ y = 1.0711413556895699\times 10^{-10}e^{0.0123604 x} $$