while loop: how to define a function when using equation with several variables?

So. I have this function as the bacteria growth:

 n (t+1) = n(t) * (1 + (alpha*(1-(n(t)/K))))

The template for the function should look like this:

 function tN = bacteriaGrowth(n0, alpha, K, N)

where n0 = initial number of bacteria (scalar)

alpha = growth rate (scalar)

K = capacity (scalar)

N = final population size (scalar, no < N < K)

tN = Time t at which population size exceeds N (scalar)

So I want to write a function that simulates the bacteria growth hour by hour and stops when the number of bacteria exceeds some fixed number, N. It must return the time t at which the population first exceeds N.

Ex: function tN = bacteriaGrowth(100, 0.4, 1000, 500) will give the output: 7

because: n0 = 100, n1 = 136, n2 = 183, n3 = 242.8, n4 = 316.3, n5 = 402.9, n6 = 499.1, n7 = 599.1, n8 = 695.2

I came up with this code, but it seems to require some (or many) adjustments.

function tN = bacteriaGrowth(n, alpha, K,N)
n = 0; 
tN = 0;
tN_after = 0;
while n < N < K
    tN = n(t) * (1 + (alpha*(1-(n(t)/K))))
    n = n + 1;
    tN_after = tN; 
    fprintf('%.4f\n', tN_after)
end

Answer 1

[Walter Roberson]

You are not changing t in your loop, so you would not be able to output the time.

while n < N < K

is the same as

while ((n < N) < K)

the first expression n < N will return either false, 0, or true, 1, so you would be checking either 0 < K or 1 < K . It is unlikely that is what you mean.

Your equation models an exponential growth. Exponential growth requires that there be something to start with, but you are initializing your population size to 0, and exponential growth from 0 is always going to remain 0.

What is the point of having parameters to a function, such as n, if you are going to overwrite them in the function without paying attention to them?

[Sandie Nhatien Vu]

Got it! You made me realize something and now l solved. Thanks!