exponential curve fitting in MATLAB for any type of x and Y data with equation y=ae^bx to calculate a and b coefficients

%code that i used is :
%program for the exponential curve fitting y=ae^bx
clc
clear
disp ('**program on exponential curve fitting y=ae^bx**')
k=xlsread("Pt-Fumion", "Sheet1");
x=input('enter value of x in matrix form:');
y=input('enter value of y in matrix form:');
n=length(x);
Y=log(y);
X=(x);
%first of all set all values to zero for addition of numbers
sumX=0;
sumY=0;
sumXY=0;
sumX2=0;
for i=1:n
    sumX=sumX+X(i);
    sumY=sumY+Y(i);
    sumXY=sumXY+X(i)*Y(i);
    sumX2=sumX2+X(i)*X(i);
end
d=[sumX n ;sumX2 sumX];  %error is displayed for this line when running the code
da=[sumY n ;sumXY sumX]; %error is displayed for this line when running the code
db=[sumXY ;sumX2 sumXY]; %error is displayed for this line when running the code
a1=det(da)/det(D);
b1=det(db)/det(d);
b=a1;
a=exp(b1);
%after finding the value of a and b the equation of line is 
fprintf('the equation of line is y=%fe^%fx',a,b)

%queries: 1. there is error in running code for concatenation of the line da and db
         %2. how can I add excel data into the input in the command window, when it asks for it
         %3. there are negative values in the y axis, is that a probelm when log is taken to excecute the code
         %4. I am doing this to to fit the data to an exponential equation and extrapolate to have a number from y axis
         %I am attaching the excel file with x and y data points

Answer 1

[Torsten]

Instead of your code (in which you linearize f giving biassed parameter estimates) use the following:

fun = @(p)p(1)*exp(p(2)*x)-y;
p0 = [1 -0.1]
p = lsqnonlin(fun,p0)
plot(x,y)
hold on
plot(x,fun(p)+y)