A crew of workers is constructing a tunnel through a mountain. Understandably, the rate of construction decreases because rocks and earth must be removed a greater distance as the tunnel gets longer. Suppose that each week the crew digs 0.95 of the distance it dug the previous week. In the first week, the crew constructed 100 m of tunnel.

a. How far does the crew dig in 10 weeks? 20 weeks? N weeks?

b. What is the longest tunnel the crew can build at this rate?