Answer
89 days
Work Step by Step
To find the number of days it take for the fish population to reach 500, we need to solve the equation $P=500$.
Solve for $t$:
$3t+10\sqrt{t}+140=500$ (Substract with 140)
$3t+10\sqrt{t}=360$ (Multiply by 3)
$9t+30\sqrt{t}=1080$ (Add with 25 to complete the square)
$9t+30\sqrt{t}+25=1105$
$(3\sqrt{t}+5)^2=1105$ (Take the square root)
$3\sqrt{t}+5=\sqrt{1105}$
$3\sqrt{t}=\sqrt{1105}-5$
$\sqrt{t}=\frac{\sqrt{1105}-5}{3}$
$t=\frac{\sqrt{1105}-5}{3}$
$t=88.6205....$
Then, it will takes 89 days.
