A hiker on the Appalachian Trail planned to increase the distance covered by 20% each day. After 7 days, the total distance traveled is 51.664 miles. Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points) Part B: What is the equation for S_n? Show all necessary math work. (3 points) Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work. (3 points)