;; (! n): natNum --> num
;; Given n, return n*(n-1)*...*2*1.
;;
(define (! n)
    (cond [(zero? n) 1]
        [else  (* n (! (sub1 n)))]))

"! Test cases:"
;
(= 2 (! 2))

(= 6 (! 3))

(= 1 (! 0))



;; rabbits: natnum num --> num
;; calculates the number of rabbits after n breeding cycles
;; assuming that each rabbit has b offspring on average
;; Start with 2 rabbits
;; Assume no deaths.

(define (rabbits n b)
  (cond 
    [(zero? n) 2]
    [else (* (+ 1 b) (rabbits (sub1 n) b))]))

"Rabbits test cases:"

(= 2 (rabbits 0 2))

(= 4 (rabbits 1 1))

(= 8 (rabbits 1 3))

(= 6250 (rabbits 5 4))