Solve the problem.
-The formula P = 0.67x2 - 0.044x + 2 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 25.856 thousand fish?
A)2002
B)2003
C)2005
D)2004

Question

Quizplus · Accepted Answer

To solve this problem, we need to substitute 25.856 for P in the equation 0.67x2 - 0.044x + 2 and solve for x.

25.856 = 0.67x2 - 0.044x + 2

Simplifying the equation, we get:

0.67x2 - 0.044x - 23.856 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b2 - 4ac)) / 2a

Where a = 0.67, b = -0.044, and c = -23.856

Plugging in the values, we get:

x = (-(-0.044) ± sqrt((-0.044)2 - 4(0.67)(-23.856))) / 2(0.67)

x ≈ 6.9 or x ≈ -5.7

Since the problem asks for a year after 1997, we need to add x to 1997 to get the year. The negative solution is not relevant since it does not make sense to have a negative number of years after 1997.

Therefore, the population will reach 25.856 thousand fish in approximately 6.9 years after 1997, which corresponds to the year 2004. Thus, the answer is D.

Solve the Problem. -The Formula P = 0.67x2 - 0.044x + 2 Models