The following polynomial approximates the rabbit population in a particular area. $R ( x ) = - 0.135 x ^ { 5 } + 2.952 x ^ { 4 } + 3500$ 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 remains stable.
B) The population increases.
C) The population decreases.

Question

Quizplus · Accepted Answer

The polynomial $R(x) = -0.135x^5 + 2.952x^4 + 3500$ initially increases due to the positive $x^4$ term dominating, indicating an increase in rabbit population over the years. The negative $x^5$ term's impact is less significant in the early years, leading to overall population growth within the 0 to 25-year range.

The Following Polynomial Approximates the Rabbit Population in a Particular R(x)=−0.135x5+2.952x4+3500R ( x ) = - 0.135 x ^ { 5 } + 2.952 x ^ { 4 } + 3500R(x)=−0.135x5+2.952x4+3500

The Following Polynomial Approximates the Rabbit Population in a Particular $R ( x ) = - 0.135 x ^ { 5 } + 2.952 x ^ { 4 } + 3500$