1. (3 pt) Michelle, WSU ME student, would like to design a multistage, water purification system that removes 1/3 of the impurity from the previous stage as the water passes through the water filter at each stage. Assume the initial impurity level (without passing the water filter) is 1. After the water passes the first stage, the impurity level becomes 1/3, and after the water passes the second stage, the impurity level becomes (1/3)2, etc. (a) Write a script to calculate the amount of remaining impurity in water after the water passes nth stage, where 1 ns20. (1 pt) (b) Plot the amount of remaining impurity in water after the water passes nth stage as a function of n, i.e, 1 n s 20. (1 pt) (c) What is the minimum number of stages that you need remove the 99% of the initial impurity? (1 pt)