4. Applications of Rec. Relations (10 points) Suppose we designed a robot that c

Question

4. Applications of Rec. Relations (10 points) Suppose we designed a robot that can build copies of itself and that it takes the robots one hour to make a copy of themselves. Assume that at hour zero we had 2 such robots. Let fn be the number of copies of the robot after n hours have passed (where n 2 0). Find a recurrence relation that represents fn 1) Find the followings( 6 points) 2) Recursive case( 4 points): = 5. Recursive Definitions (22 points) Write down the first 5 elements of the sequence, then give a recursive definition for an (where n 1) an = on 20 a) First 5 elements b) Base case: ao c 0). c) Recursive case: an 2) an = (-1)n a) First 5 elements: b) Base case: a0 = c) Recursive case: an- a1.

Explanation / Answer

Here's the solution, do comment out if you have any doubts. Thumbs up if this helps!

4. 1. a) f0=2, f1=4, b) f2=8, c) f3=16

2. fn=2^(n+1) as we can see that for every hour, it doubles

5. an=5n+20

a0=20, a1=25, a2=30, a3=35, a4=40

Base case, a0=20

Recursive case, an=a(n-1)+5

2. a0=1, a1=-1, a2=1, a3=-1, a4=1

Base case : a0=1

Recursive Case : an=-a(n-1)

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.