1. **State the problem:** We want to find a function $f(m)$ that gives the number of miles of paved roads in country Y $m$ years after 2017. 2. **Identify given information:** - In 2017, there were 500 miles of paved roads. - Starting in 2018, the country builds 6 miles of new paved roads each year. - $m$ represents the number of years after 2017. 3. **Analyze the situation:** - At $m=0$ (the year 2017), the number of miles is 500. - Each year after 2017, the number of miles increases by 6 miles. 4. **Form the function:** - The function should start at 500 when $m=0$. - It should increase by 6 miles for each additional year $m$. - This is a linear function of the form $$f(m) = 500 + 6m$$ 5. **Check the options:** - A. $6 + 2017m$ (incorrect, starts at 6 and multiplies by 2017) - B. $2017 + 6m$ (incorrect, starts at 2017 miles) - C. $500 + 6m$ (correct, matches initial miles and yearly increase) - D. $2018 + 6m$ (incorrect, starts at 2018 miles) **Final answer:** The correct function is $$f(m) = 500 + 6m$$