Final answer:
To determine the source of the lake sediment, analyze the biotite grains and compare their ages with potential source rocks. Consider factors like water flow and geological features.
Step-by-step explanation:
To determine where the lake sediment came from, you can analyze the biotite grains collected from the lake bottom. In this case, there are two potential sources: metamorphic rocks to the west and granites to the south. To find the ages of these potential sources, you can use radiometric dating methods such as carbon dating or potassium-argon dating.
By comparing the ages of the potential source rocks with the ages of the biotite grains, you can determine which source is most likely responsible for the sediment in the lake. Additionally, you can consider other factors such as the direction of water flow or any geological features that could influence the distribution of sediment in the lake.