Linear Approximation

Linear Approximation

Here I will attempt to use linear approximation to estimate the value of $ln(1.07)$

The first thing you need to do when performing a linear approximation is set up an equation with known numbers as variables:

$y = f(x) = ln(x)$ here we have turned 1.07 into “x”.

Now take the derivative of either side; $dy = \frac{1}{x} dx$ when x = 1 and dx = 0.07

$dy = \frac{1}{1} (0.07) = 0.07$

ln(1.07) = f(1.07) because our f(x) function was equal to ln(x), so we know in this case, that x = 1.07, after all, it was given in the problem.

$f(1.07) \approx f(1) + dy = 0 + 0.07 = 0.07.$