Question: Select the correct point on the graph. A golf course recently added bass to several of its ponds. The population of bass is currently $500$ and is expected to increase by at least $20\%$ every year. The bass population can be represented after $x$ years by this inequality. $$y \geq 500(1.2)^x$$ At the time the bass were added, the golf course managers determined that this inequality represents the maximum yearly number of bass that the ponds could support after $x$ years. $$y \leq 2000 - 10x$$ Which point on the graph reveals a possible number of bass, $y$, living in the ponds?

1. **State the problem:** We need to find a point $(x,y)$ that satisfies both inequalities: $$y \geq 500(1.2)^x$$ and $$y \leq 2000 - 10x$$ This means the bass population $y$ after $x$ years must be at least $500(1.2)^x$ and at most $2000 - 10x$. 2. **Understand the inequalities:** - The first inequality $y \geq 500(1.2)^x$ shows the minimum bass population growing exponentially. - The second inequality $y \leq 2000 - 10x$ shows the maximum bass population decreasing linearly. 3. **Find possible points:** We want to find values of $x$ and $y$ such that: $$500(1.2)^x \leq y \leq 2000 - 10x$$ 4. **Check example points:** - For $x=0$: - Minimum bass: $500(1.2)^0 = 500$ - Maximum bass: $2000 - 10(0) = 2000$ - So $y$ can be any value between $500$ and $2000$. - For $x=5$: - Minimum bass: $500(1.2)^5 = 500 \times 2.48832 = 1244.16$ - Maximum bass: $2000 - 10(5) = 2000 - 50 = 1950$ - So $y$ can be any value between $1244.16$ and $1950$. 5. **Interpretation:** Any point $(x,y)$ where $y$ is between these two bounds is possible. 6. **Conclusion:** The correct point on the graph must satisfy: $$500(1.2)^x \leq y \leq 2000 - 10x$$ This means the bass population $y$ is at least the exponential growth minimum and at most the linear maximum after $x$ years. **Final answer:** Any point $(x,y)$ that satisfies the above inequalities is a possible number of bass living in the ponds.