An ecologist is studying the populations of two types of fish in Lake Shasta. There are currently 2,825 Bluegills in the lake and they are increasing at a rate of 400 Bluegills per year. The data gathered on the Rainbow Trout population is shown in the table below. At this rate, how long will it take for the Bluegill population to be the same as the Rainbow Trout population? What will be the population of each fish at that time? EXPLAIN HOW YOU ARRIVED AT YOUR SOLUTION. * Rainbow Trout population
Years Population
0 5,750
1 5,500
3 5000

Answer is in the file below

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answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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