解：?$(1)$?當(dāng)?$x＜40$?時(shí)，設(shè)?$y$?與?$x$?的函數(shù)關(guān)系式為?$y=kx+b$?
由圖可得，?$\begin {cases}{10k+b=2000 } \\{30k+b=3000} \end {cases}$?，解得?$\begin {cases}{k=50}\\{b=1500}\end {cases}$?
即當(dāng)?$x＜40$?時(shí)，?$y$?與?$x$?的函數(shù)關(guān)系式為?$y=50x+1500$?
當(dāng)?$x=40$?時(shí)，?$y=50×40+1500=3500$?
∵在第?$40$?天后每天的需水量比前一天增加?$100$?千克
∴第?$41$?天需水量為?$3600$?千克
當(dāng)?$x≥40$?時(shí)，設(shè)?$y$?與?$x$?的函數(shù)關(guān)系式為?$y=mx+n$?
?$\begin {cases}{40m+n=3500 } \\{41m+n=3600} \end {cases}$?，解得?$\begin {cases}{m=100}\\{n=-500}\end {cases}$?
即當(dāng)?$x≥40$?時(shí)，?$y$?與?$x$?的函數(shù)關(guān)系式為?$y=100x-500$?
?$(2)$?將?$y=4000$?代入?$y=100x-500$?，得?$4000=100x-500$?
解得?$x=45$?
∴應(yīng)從第?$45$?天開始進(jìn)行人工灌溉
