$4\mathrm{.}4\mathrm{.}6$ For the time$-$drawdown data listed below for a confined aquifer, calculate T and S using Jacob's approximation. After computing Tand S$,$ check to see that the basic assumption of this approximation is satisfied. For the values of T and S that you computed, after how many minutes of pumping would Jacob's approximation be valid? The discharge is Q $=1,500$ gpm and the radius r $=300$ft

Time after pumping started $($min$)$

Drawdown $($ft$)$

$1$

$0\mathrm{.}45$

$2$

$0\mathrm{.}74$

$3$

$0\mathrm{.}91$

$4$

$1\mathrm{.}04$

$6$

$1\mathrm{.}21$

$8$

$1\mathrm{.}32$

$10$

$1\mathrm{.}45$

$30$

$2\mathrm{.}02$

$40$

$2\mathrm{.}17$

$50$

$2\mathrm{.}30$

$60$

$2\mathrm{.}34$

$80$

$2\mathrm{.}50$

$100$

$2\mathrm{.}67$

$200$

$2\mathrm{.}96$

$400$

$3\mathrm{.}25$

$600$

$3\mathrm{.}41$

$800$

$3\mathrm{.}50$

$1,000$

$3\mathrm{.}60$

$1,440$

$3\mathrm{.}81$