Question

The formula P = 0.68x2 - 0.048x + 1 models the approximate population P, in thousands, for a species of fish in a local pond, x years after 1997. During what year will the population reach 33.984 thousand fish?

Answer 1

Answer:

The answer to your question is 2184

Step-by-step explanation:

Data

Equation    P(x) = 0.68x² - 0.048x + 1

x = years

population = 33984

Process

1.- Substitute the population in the equation

                   33984 = 0.84x² - 0.048x + 1

2.- Equal to zero

                   0.84x² - 0.048x + 1 - 33984 = 0

3.- Simplify

                    0.84x² - 0.048x - 33983 = 0

4.- Solve for x

$x = \frac{0.048 +- \sqrt{(0.048^{2}) - (4)(0.84)(-33982)}}{2(0.84)}$

$x = \frac{0.048 +- \sqrt{337.9}}{1.68}$

x1 = 201.2

x2 = -201.2

Only x1 is correct because time can not be negative

5.- Calculate the year

Year = 1997 + 201

Year = 2184