Question

Solve the problem.

Answer 1

Answer:

The population reaches 42,336 fish in 2258

Step-by-step explanation:

Given:

$P = 0.62x^2 - 0.043x + 3$

To Find:

Time taken  to reach 42,336 = ?

Solution:

According to the question  x is the number of years after which the population .

Then

$42336 = 0.62x^2 - 0.043x + 3$

$0 = 0.62x^2 - 0.043x + 3- 42333$

$0.62x^2 - 0.043x -42333$ = 0

Solving using quadratic formula

$x =\frac{ -b\pm \sqrt{b^2 -4ac}}{2a}$

$x =\frac{ -(-0.043)\pm \sqrt{(-0.043) -4(0.62)(42333)}}{2(42333)}$

$x =\frac{ -(-0.043)\pm \sqrt{(0.001849) -0.10664}}{84666}$

x=261.337                    x=−261.268

Neglecting the   negative value we get

x = 261.337

x =  261 approx

261 years after  1997  =  2258