How to use log/exponential forms for line of best fit?

I created a graph that contains a line of best fit using the linear form y = ax+b. It will tell me the values of a and b in the command window. However, I also want to add a line of best fit using the log/exponential form y = Ce^dx and display the values of C and d in the command window. How can I do so?

rideData; % contains the data for speed and distance

figure(1);
plot(speed, distance, "o");
p = polyfit(speed, distance, 1);
f = polyval(p, speed);

hold on
plot(climb, f, 'r');
xlabel('speed');
ylabel('distance');

slope = p(1);
fprintf('a = %f\n', slope);
intercept = p(2);
fprintf('b = %f\n', intercept);

Answer 1

[Star Strider]

You could do a log transformation, however that distorts the errors and (unless the errors are negligable), a less than optimum fit.

I prefer something like this:

eqn = @(b,x) b(1).*exp(b(2).*x);

x = speed;
y = distance;

B = fminsearch(@(b) norm(y - eqn(b,x)), [1; -1]);
fexp = eqn(B,x);

figure
plot(x, fexp)
xlabel('speed');
ylabel('distance');