A 2 A plant double the number of its buds every day and produce a

supplementary. The figure f: N -> N describe the number of buds by n

Days ago. On the first day the plant has a bud, i.e. f(1) = 1.

(a) Give a recursive description of fan.

(b) Determine f(n) for n 5.

(c) Make a conjecture for the explicit form of f and prove this

with complete induction.

(d) How many buds does the plant have after 10 days?