How to calculate $f(x)$ from exponential function in graph?

Question

Given an exponential graph image of $f(x)$, how do you calculate $f(x)$?

Answer 1

There are native ways to fit the function as noted in this posts. Logarithmic transformations will distort the problem.

Least squares solution for $y=ax^{b}$ after logarithmic transformation

Linearize $y=c +ax^{b}$

Least Square Approximation for Exponential Functions

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Suppose you want to use the functional form $y=ae^{bx}$.

From the boundary point $(0,4)$, we know $a=4$. Now solve for $b$ using the second endpoint $(10,24)$: $$ 4 e^{10b} = 24 $$ to find $$ b = \frac{\ln 6}{10} $$

Answer 2

If it is exponential then you can use the logarithms to fit a line since $\ln(e^x) = x$.