Trouble with vector length

I'm having trouble plotting a population vs time model; I keep getting the error "vectors must be the same length." I need my x-axis to show population from 1804-2300, but I had to use 1-496 as my time values in the code. I think linspace needs to come into play somewhere, but it doesn't seem to be working. Note: there very well may be other issues in my code. Thanks in advance for your help!

%Variable key
%t is the number of years the model runs, from 1804-2300.
t = [1:496]
%r is the population growth rate.
r = 0.01
%K is the human carrying capacity in billions of people.
K = 10
%P0 is the human population in billions at the time the model begins.
P1 = 1
%A is the 
A = (K-P1)/P1
%P is the human population in the model in billions of people.
P = (K)./(1+A*exp(-r*t))

%Let 1804, the year the model begins, equal year 1.
t(1) = 1

%Loop ensures that the the population data cycles through the model for every year and stops 496 years after the model begins, at 2300.
for  i = 1:496
    if t(i) <= 496
       % Population growth (pop_g)
       r = 0.01;
    else
       break
    end
    
   %If-else clause takes into account the human carrying capacity of 10 billion by lowering the growth rate after the carrying capacity is reached.
   if P <=10
       r = 0.01
   else
      r = .008
   end
   
   %Calculate the next year of population growth using the population that was just aquired.
   P(i+1) = (r*P(i)) + P(i)
end

%Plot the population model data.
figure
        hold on
        t = linspace(1804,2300)
        plot (t,P)
        title ('Model Population Test Graph')
        legend ('Model Population')
        xlabel ('Years')
        ylabel ('Population')
        grid on

Answer 1

[KSSV]

To plot the xdata and ydata should be same. In your case t and P are of different size. Get them to same size.

%Variable key
%t is the number of years the model runs, from 1804-2300.
t = [1:496] ;
%r is the population growth rate.
r = 0.01 ;
%K is the human carrying capacity in billions of people.
K = 10 ;
%P0 is the human population in billions at the time the model begins.
P1 = 1 ;
%A is the
A = (K-P1)/P1 ;
%P is the human population in the model in billions of people.
P = (K)./(1+A*exp(-r*t)) ;
%Let 1804, the year the model begins, equal year 1.
t(1) = 1;
%Loop ensures that the the population data cycles through the model for every year and stops 496 years after the model begins, at 2300.
for  i = 1:496
    if t(i) <= 496
        % Population growth (pop_g)
        r = 0.01; 
    else
        break
    end
    
    %If-else clause takes into account the human carrying capacity of 10 billion by lowering the growth rate after the carrying capacity is reached.
    if P <=10
        r = 0.01 ;
    else
        r = .008 ;
    end
    
    %Calculate the next year of population growth using the population that was just aquired.
    P(i+1) = (r*P(i)) + P(i) ;
end
%Plot the population model data.
figure
hold on
t = linspace(1804,2300,length(P)) ;
plot (t,P)
title ('Model Population Test Graph')
legend ('Model Population')
xlabel ('Years')
ylabel ('Population')
grid on

[Amelia Baran]

Thank you so much!

[madhan ravi]

Square brackets are superfluos:

t=1:496;