Question 919253
The population is given by {{{f(x)=0.8x^2-12.8x+54.2}}} with {{{x}}}= number of years after 1989.
The maximum/minimum for a quadratic function {{{g(x)=ax^2+bx+c}}} happens for {{{x=-b/2a}}} .
(It is a minimum if {{{a>0}}}, a maximum if {{{a<0}}} .
In this case, {{{a=0.8}}} and {{{b=-12.8}}} ,
so there is a minimum for{{{x=-(-12.8)/(2*0.8)=12.8/1.6=8}}} ,
and {{{x=8}}} corresponds to {{{1989+8=1997}}} .