Question 339926
{{{F=1000(30+15t-t^2)}}}
==
1. The fish population will again be the same as on January 1, 2002

January 1,2002 means t=0
when t=0, F=30,000
so you want to know when {{{F=30000=1000(30+15t-t^2)}}}
which means {{{30000/1000=30+15t-t^2}}}
{{{0=15t-t^2=(15-t)t}}}
t=0 or t=15
answer t=15 years from Jan 1, 2002 or January 1, 2017
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2. All the fish in the lake will die after 'approximately' 
You basically want to know t, for F=0
{{{F=1000(30+15t-t^2)}}}
{{{0=1000(30+15t-t^2)}}}
{{{0=30+15t-t^2}}}
use quadratic equation  with a=-1, b=15, c=30
{{{t=(-15-sqrt(15^2-4(-1)30))/(2(-1))=16.79}}} or {{{t=(-15+sqrt(15^2-4(-1)30))/(2(-1))=-1.79}}}

answer: 16.79 years after january 1, 2002 or roughly Sept 14,2018