Using logs to find a model

The idea

Taking logs turns curves into straight lines. $y = ax^n$ gives $\log y = \log a + n\log x$: plot $\log y$ against $\log x$, gradient $n$, intercept $\log a$. $y = ab^x$ gives $\log y = \log a + x\log b$: plot $\log y$ against $x$.

1. Take logs of both sides and match to $Y = mX + c$.
2. Read the gradient and intercept from the line.
3. Undo the logs: $a = 10^{\text{intercept}}$.

Watch out The intercept is $\log a$, not $a$: raise $10$ to it.