CSE341 -- Assignments -- Miranda warmup

Due 17 May 2000.

This is a small assignment to give you some experience with Miranda.

Submission directions: Please turn in both printed and electronic copies of your code. The print submission is due in class on the due date above. You may e-mail the electronic copies to Keunwoo (klee@cs) anytime the same day. For full credit, you must follow the submission guidelines.

Write and test a recursive Miranda function intersect that takes two lists and returns a list of those elements that are in both of the arguments. What is the type of this function?
Write and test a Miranda function to find the two roots of the quadratic expression a*x^2 + bx + c = 0 for parameters a, b, and c. What is the type of this function?
Write a Miranda function compound that calculates compound growth. The function should take a start year, a start amount, and a growth rate, and return an infinite list of tuples. Each tuple should be the year and the amount for that year. (The first tuple in the list will just consist of the start year and the start amount.)
For example, here is an expression to compute the the amount of money in a savings account, starting with $1 in the year 2000, at 5% interest:
```
compound 2000 1 0.05
```
This evaluates to:
Hint: a useful function, to avoid having to be quick with control-c when testing, is take, which returns the first n elements of a list. Thus
```
take 4 (compound 2000 1 0.05)
```
evaluates to:
```
[(2000,1), (2001,1.05), (2002,1.1025), (2003,1.157625)]
```
Now define a variable population that is the infinite list of yearly total populations of the earth, assuming 6 billion people starting in 1999 and an annual growth rate of 1.3%. (This actually should provide reasonable estimates in the short term, but not in the long term ... however, this is just a Miranda exercise, rather than an exercise in realistic modelling.)
Using population, find the year in which the population will have doubled (to 12 billion).