1. **State the problem:** We are given a population function $$f(x) = x^3 - x^2 - 4x + 4$$ where $$x$$ is the number of years from now. We need to find the population 8 years from now, i.e., find $$f(8)$$. 2. **Formula used:** To find the population at a specific year $$x$$, substitute $$x$$ into the function: $$f(x) = x^3 - x^2 - 4x + 4$$ 3. **Calculate $$f(8)$$:** $$f(8) = 8^3 - 8^2 - 4(8) + 4$$ 4. **Simplify step-by-step:** $$8^3 = 512$$ $$8^2 = 64$$ So, $$f(8) = 512 - 64 - 32 + 4$$ 5. **Perform the arithmetic:** $$512 - 64 = 448$$ $$448 - 32 = 416$$ $$416 + 4 = 420$$ 6. **Final answer:** The population 8 years from now will be $$420$$.