Question $3$

It is known that the data tabulated below can be modeled by the following equation:

$x=e^{\frac{y-b}{a}}$

where a and b are parameters. Linearize this equation to determine a and $b.$ Using the determined values of a and $b,$ show both the linear and non$-$linear equations. Based on your analysis, predict the value of $y$ at $x=3\mathrm{.}5.$ Please use six decimal points in all your calculations.

$\backslash$table$[[x,1,2,3,4,5],[y,0\mathrm{.}5,2,2\mathrm{.}9,3\mathrm{.}5,4]]$