Answer:
2007
Step-by-step explanation:
we have
[tex]p(x)=0.65x^{2} -0.047x+2[/tex]
This is a vertical parabola open upward
The vertex represent a minimum
p(x) is the population in thousands for a species of fish
x is the number of years since 1997
Remember that p(x) is in thousands
so
If the population reach 66,530 fish
then
the value of p(x) is equal to
p(x)=66.53
substitute in the quadratic equation
[tex]66.53=0.65x^{2} -0.047x+2[/tex]
[tex]0.65x^{2} -0.047x+2-66.53=0[/tex]
[tex]0.65x^{2} -0.047x-64.53=0[/tex]
Solve the quadratic equation by graphing
The solution is x=10 years
see the attached figure
therefore
Find the year
Adds 10 years to 1997
1997+10=2007
