Need Help with while loop

The code I have so far works but I think I missing something with time as a factor. I'm not sure how to utilize that part. Any help would be much appreciated.

The problem statement is this: A type of pathogenic bacteria in a lake under optimal conditions double their number (growth rate of p = 1) every 20 hours. Starting with n0 bacteria at time zero, there are n1=n0(1+p) bacteria after 20 hours, n2=n1(1+p) bacteria after 40 hours, and so on. For this particular type of pathogenic bacteria and lake, the lake is not safe to swim in if the bacteria 2 population density exceeds 104 bacteria per ml. Write a MATLAB program that will determine how long it will take for an initial pathogenic bacteria level of n0=100 per ml to reach an unsafe level of n = 104 per ml. The program should display the time in days it takes for the bacteria population density to reach or exceed the unsafe level.

So far the code I have created is this: I understand I'm missing the display I know how to do that part, Its just the other parts I'm missing in my statement that I don't understand to put in the code:

clear;
clc;

% define max bacteria density level that is unsafe for swimming per mL
n_max = 10^4;

% intitialize(else 1st iteration,n_sum, p will be undefined)
n_sum = 0;
p =0;

% while loop with condition defined
while (n_sum <= n_max)
    % update counter
    p = p + 1;
    n_sum =  n_sum + p;
end

[dpb]

Suggestion--write the algebraic equations and solve it instead (unless the requirement is the loop, too)...

[Jason]

Yea I have to use a while loop.. that's why I'm stuck at where I'm at

[per isakson]

"(growth rate of p = 1) every 20 hours" &nbsp and &nbsp p = p + 1; % update counter &nbsp defines two different meanings of p, which is confusing.

[dpb]

It (the code definition, that is) is also incorrect, not just confusing.

Second suggestion--rethink what the rate equation is from the problem description and factor that into the formulation...even if the coded solution is to be the iterative one, writing the algebra should help to see how to implement it.