I have a problem here I am working on that is asking me to "Find an equation of the line through the first and last data points. Then find an exponential model $P(x)$ for the population data. Use natural logs of $y$ coordinates to find the equation of the regression line."
The population data: $(0,10), (1,15), (2,23), (3,35), (4,54)$
I just started by finding the equation of the secant line through the first and last points and got $$y = 11x + 10$$
From here I wasn't exactly sure what to do, after a bit of looking around I looked at a hint to the problem which stated "Fitting a line to the plot of the natural logarithms is equivalent to fitting an exponential function to the original data. Allow $y = \ln (P(x))$, then find a line of best fit.
From this suggestion I equated $$11x + 10 = y = \ln (P(x)) \implies P(x) = e^{(11x + 10)} = e^{11x} + e^{10}$$
However this doesn't seem to be correct. Any help would be greatly appreciated.