Question

Given the following MATLAB code,

k=0;
while k^k<=2^k;
k=k+1;
end
k what is the value of k after executing the code?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Answer 1

After executing the MATLAB code, the loop stops when the condition is no longer satisfied, which is for k=3. Therefore, the final value of k is 3.

Step-by-step explanation:

The given MATLAB code executes a while loop that continues as long as the condition k^k <= 2^k is true. Initially, k is set to 0. During each iteration of the loop, k is incremented by 1, and the condition is checked again. This process will continue until k^k is greater than 2^k, at which point the loop will terminate, and the value of k at that time will be the final value.

Let's iterate manually to find when the loop will stop:

• For k=0: 0^0 (which is 1) <= 2^0 (which is 1) - the loop continues.
• For k=1: 1^1 (which is 1) <= 2^1 (which is 2) - the loop continues.
• For k=2: 2^2 (which is 4) <= 2^2 (which is 4) - the loop continues.
• For k=3: 3^3 (which is 27) > 2^3 (which is 8) - the loop stops.

After executing the code, the final value of k is 3, so the correct answer is (D) 3.