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?

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

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

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

x² + 11x + 18 < 0  

[-11 ± sqrt(121 - 72)]/2 = (-11 ± 7)/2  

solution: (-9, -2)

step-by-step explanation: