This assignment is due at the start of class on Wednesday, Sept 20.

I need help on the actual code, especially the looping structure from within MATLAB. Homework Class 8. This assignment is due at the start of class on Wednesday, Sept 20. Task 4. Input two variables, A and B. Test each variable to ensure that they are positive integers. Develop an algorithm to determine the smallest power of A that is greater than B. For example, A=2 and B=9. A=2; A^2=4; A^3=8; A^4=16. So, we want to return the value “4” since A^4=16>9. Note, this requires a looping structure. Document your algorithm using both a flow diagram and pseudocode. Now prepare a MATLAB script for this problem called Power_Calculator.m. Your program should input A and B, calculate the smallest power of A that is greater than B, and output the smallest power. Add comments to your program, such that if someone typed “help Power_Calculator” in the Command Window, comments would be displayed in the Command Window that describe what the program is supposed to do, the types of inputs, and the types of outputs. You will also need to test to see if A and B are positive integers. Save your MATLAB file and submit it, plus your algorithms, through the submission box. Testing for integers. This is not straightforward. For example, if you use the MATLAB function “isinteger”, for A=9, the function “isinteger(A)” would return a value of false. This is because the input for A is entered as floating point by default, and not as an integer. So values of 1, 2.3, 9, 10.145, etc., when tested with the “isinteger” function, all return a value of 0 (or false). The easiest way to test to see if a number is an integer is to use the “mod” function. For r=mod(A,n), A is the dividend, n is the divisor, and r is the remainder after A is divided by n. So if A=3.14, then for b=mod(A,1), b=0.14 which is the remainder. But if A is an integer such as A=34, then for b=mod(A,1), b=0. (Note: b is a real number, equal to zero, and not a Boolean “false” output). So to test if the values are integers, as a condition, use “mod(A,1)==0” and “mod(B,1)==0.

The Correct Answer and Explanation is:

✅ MATLAB Code: Power_Calculator.m

matlabCopyEdit% Power_Calculator.m
% This script calculates the smallest power of A such that A^n > B.
% Inputs: Two positive integers A and B
% Output: Smallest integer n such that A^n > B

% Prompt the user for input
A = input('Enter a positive integer value for A: ');
B = input('Enter a positive integer value for B: ');

% Validate that A and B are positive integers
if (A <= 0 || B <= 0 || mod(A,1) ~= 0 || mod(B,1) ~= 0)
    error('Both A and B must be positive integers.');
end

% Initialize variables
n = 0;
power = 1;

% Loop to find the smallest power such that A^n > B
while power <= B
    n = n + 1;
    power = A^n;
end

% Display result
fprintf('The smallest integer n such that A^n > B is: %d\n', n);

💡 Explanation

This MATLAB program determines the smallest power of a given positive integer A that results in a value greater than another positive integer B. The task is to find the smallest integer n such that A^n > B. The script is user-interactive and includes input validation to ensure that both numbers are indeed positive integers.

MATLAB by default reads numeric inputs as floating-point values. This behavior causes the built-in function isinteger() to be ineffective for checking if user-entered values like 3 or 7 are integers. To handle this, the script uses the mod function. The expression mod(A,1) == 0 checks whether there is a remainder when A is divided by 1. If the result is zero, the number is an integer.

Once the inputs are validated, the program enters a loop. The variable n starts at zero and increases by one during each loop iteration. The current power of A^n is calculated and compared with B. If A^n is less than or equal to B, the loop continues. The moment A^n exceeds B, the loop ends, and the value of n is printed.

This approach ensures a straightforward and efficient solution using basic loop constructs and conditionals. The logic is clean and easy to follow, making the program suitable for beginners who are learning about loops, conditionals, and input validation in MATLAB.