Answer:
The population reaches 42,336 fish in 2258
Step-by-step explanation:
Given:
[tex]P = 0.62x^2 - 0.043x + 3[/tex]
To Find:
Time taken to reach 42,336 = ?
Solution:
According to the question x is the number of years after which the population .
Then
[tex]42336 = 0.62x^2 - 0.043x + 3[/tex]
[tex]0 = 0.62x^2 - 0.043x + 3- 42333[/tex]
[tex]0.62x^2 - 0.043x -42333[/tex] = 0
Solving using quadratic formula
[tex]x =\frac{ -b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
[tex]x =\frac{ -(-0.043)\pm \sqrt{(-0.043) -4(0.62)(42333)}}{2(42333)}[/tex]
[tex]x =\frac{ -(-0.043)\pm \sqrt{(0.001849) -0.10664}}{84666}[/tex]
x=261.337 x=−261.268
Neglecting the negative value we get
x = 261.337
x = 261 approx
261 years after 1997 = 2258
