Solve the problem
-The following polynomial approximates the rabbit population in a particular area. $$R ( x ) = - 0.121 x ^ { 5 } + 3.013 x ^ { 4 } + 3500$$ where x is the number of years from year 0. Use a graphing calculator to describe the rabbit population from the years 0 to 25.
A) The population decreases.
B) The population remains stable.
C) The population increases.

Question

Quizplus · Accepted Answer

The leading term of the polynomial $-0.121x^5$ dictates the long-term behavior of the function. Despite the negative coefficient, the even-powered term $3.013x^4$ will dominate the graph's shape for large values of $x$, causing the population to initially increase. Given the polynomial's structure, the population will increase over the years, especially noticeable in the early years (0 to 25) before any potential long-term decline due to the fifth-degree term. Graphing the polynomial from years 0 to 25 will show an increasing trend in the rabbit population.

Solve the Problem -The Following Polynomial Approximates the Rabbit Population R(x)=−0.121x5+3.013x4+3500R ( x ) = - 0.121 x ^ { 5 } + 3.013 x ^ { 4 } + 3500R(x)=−0.121x5+3.013x4+3500

Solve the Problem
-The Following Polynomial Approximates the Rabbit Population $R ( x ) = - 0.121 x ^ { 5 } + 3.013 x ^ { 4 } + 3500$