The following polynomial approximates the shark population in a particular area. $R ( x ) = - 0.021 x ^ { 5 } + 4.133 x ^ { 4 } + 200$ where x is the number of years from year 0. Use a graphing calculator to describe the shark population from the years 0 to 25.
A) The population increases.
B) The population remains stable.
C) The population decreases.

Question

Quizplus · Accepted Answer

The polynomial has a positive leading coefficient for the $x^4$ term, which dominates the behavior of the polynomial for the given range, indicating an overall increase in the shark population from year 0 to 25.

The Following Polynomial Approximates the Shark Population in a Particular R(x)=−0.021x5+4.133x4+200R ( x ) = - 0.021 x ^ { 5 } + 4.133 x ^ { 4 } + 200R(x)=−0.021x5+4.133x4+200

The Following Polynomial Approximates the Shark Population in a Particular $R ( x ) = - 0.021 x ^ { 5 } + 4.133 x ^ { 4 } + 200$