Chapter 5 - Section 5.1 - Introduction to Polynomials and Polynomial Functions - Exercise Set - Page 326: 71

See below.

The leading coefficient of $f$ is $-1$, which is negative and the degree of $f$ is $4$, which is even. Thus the function falls to the left and falls to the right. Thus at one point $f$ is going to be $0$, thus the population will become extinct at one point.