Chapter 5 - Section 5.1 - Introduction to Polynomials and Polynomial Functions - Exercise Set - Page 326: 83

See below.

The leading coefficient of $f$ is $-0.125$, which is negative and the degree of $f$ is $5$, which is odd. Thus the function falls to the right. Thus at one point $f$ is going to be $0$, so once the population will become extinct.