Answer
The fish population will reach 500 after 89 days.
Work Step by Step
$P=3t+10\sqrt t+140$
$P=500$, find t
$500=3t+10\sqrt t+140$
$3t+10\sqrt t-360=0$
Let $a=\sqrt t$, a>0 then $3a^{2}+10a-360=0$
$a=\frac{-10+\sqrt (10^{2}-4\times3\times(-360))}{2\times3}=\frac{-10+\sqrt 4420}{6}=9.41$
or $a=\frac{-10-\sqrt (10^{2}-4\times3\times(-360))}{2\times3}=\frac{-10-\sqrt 4420}{6}=-12.75$(eject)
$a=9.41$, then $\sqrt t=9.41$, so $t=9.41^{2}=88.5481\approx89$days
So the fish population will reach 500 after 89 days
