Solve the problem.
-The formula $P = 0.61 x ^ { 2 } - 0.041 x + 3$ 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 24,714 fish?
A) 2005
B) 2004
C) 2003
D) 2002

Question

Quizplus · Accepted Answer

Given the formula $P = 0.61x^2 - 0.041x + 3$, where $P$ is the population in thousands and $x$ is the number of years after 1997, we need to find the year when the population reaches 24,714 fish. First, convert 24,714 fish to thousands to match the units in the formula, which gives $P = 24.714$. Then, solve the equation $0.61x^2 - 0.041x + 3 = 24.714$ for $x$. Solving this equation gives $x \approx 6$. Since $x$ is the number of years after 1997, the year when the population reaches 24,714 is $1997 + 6 = 2003$.

Solve the Problem P=0.61x2−0.041x+3P = 0.61 x ^ { 2 } - 0.041 x + 3P=0.61x2−0.041x+3

Solve the Problem $P = 0.61 x ^ { 2 } - 0.041 x + 3$