Question

the quadratic p(x)=.65x squared - .047x +2 models the population p(x) in thousands for a species of fish in a local pond, x years after 1997. during what year will the population reach 66,530 fish

Answer 1

Answer:

2007

Step-by-step explanation:

we have

$p(x)=0.65x^{2} -0.047x+2$

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

$66.53=0.65x^{2} -0.047x+2$

$0.65x^{2} -0.047x+2-66.53=0$

$0.65x^{2} -0.047x-64.53=0$

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