A base$-$year trip$-$generation study obtained the data shown relating to the daily person$-$trip productions per dwelling unit $)$ and residential density $(x$ dwelling units per acre$).$

$\backslash$table$[[Y,3\mathrm{.}5,6\mathrm{.}5,4\mathrm{.}0,2\mathrm{.}2],[x,30\mathrm{.}0,10\mathrm{.}0,50\mathrm{.}0,70\mathrm{.}0]]$

$($a$)$ Calibrate and plot the relationship $Y=(a+bx{)}^{-1}.$

$($b$)$ Apply your answers to part $($a$)$ to the following situation: A residential zone I has an area of $500$ acres and contains $7500$ dwelling units. Two zones and $L)$ are competing for the trips produced by I. Given the following information, calculate the trip interchange volumes $Q_{IJ}$ and $Q_{IL}$ if $W_{IJ}=10,W_{IL}=8,lnF=-1\mathrm{.}5lnW,A_J=0\mathrm{.}5A_L$ and all $K_{IJ}=1\mathrm{.}0.$

PLEASE DO PART A MATHMATICALLY NOT ON EXCEL