$17\mathrm{.}13$ An investigator has reported the data tabulated below. It is known that such data can be modeled by the following equation

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

where a and $b$ are parameters. Use a transformation to linearize this equation and then employ linear regression to determine a and $b.$ Based on your analysis predict $y$ at $x=2\mathrm{.}6.$

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