clc
clear 

x_a = [25 30 35 40 45];
y_a = [5 260 480 745 1100];

% Power fit: y = a*x^b  → log(y) = log(a) + b*log(x)
p_a = polyfit(log(x_a), log(y_a), 1);
b_a = p_a(1);
a_a = exp(p_a(2));

x_fit = linspace(min(x_a), max(x_a), 100);
y_fit_a = a_a * x_fit.^b_a;

figure;
plot(x_a, y_a, 'ro', 'MarkerSize',8, 'LineWidth',2); hold on;
plot(x_fit, y_fit_a, 'b-', 'LineWidth',2);
title('Part (a): Power Fit');
xlabel('x'); ylabel('y');
legend('Data','Power Fit','Location','northwest');
grid on;
 
x_b = [2.5 3 3.5 4 4.5 5 5.5 6 7 8 9 10];
y_b = [1500 1220 1050 915 810 745 690 620 520 480 410 390];

% Exponential fit: y = a*e^(bx) → log(y) = log(a) + b*x
p_b = polyfit(x_b, log(y_b), 1);
b_b = p_b(1);
a_b = exp(p_b(2));

x_fit = linspace(min(x_b), max(x_b), 100);
y_fit_b = a_b * exp(b_b * x_fit);

figure;
plot(x_b, y_b, 'ro', 'MarkerSize',8, 'LineWidth',2); hold on;
plot(x_fit, y_fit_b, 'b-', 'LineWidth',2);
title('Part (b): Exponential Fit');
xlabel('x'); ylabel('y');
legend('Data','Exponential Fit','Location','northeast');
grid on;

x_c = [550 600 650 700 750];
y_c = [41.2 18.62 8.62 3.92 1.86];

% Exponential fit again
p_c = polyfit(x_c, log(y_c), 1);
b_c = p_c(1);
a_c = exp(p_c(2));

x_fit = linspace(min(x_c), max(x_c), 100);
y_fit_c = a_c * exp(b_c * x_fit);

figure;
plot(x_c, y_c, 'ro', 'MarkerSize',8, 'LineWidth',2); hold on;
plot(x_fit, y_fit_c, 'b-', 'LineWidth',2);
title('Part (c): Exponential Fit');
xlabel('x'); ylabel('y');
legend('Data','Exponential Fit','Location','northeast');
grid on;

fprintf('Part (a): y = %.4f * x^{%.4f}\n', a_a, b_a);
fprintf('Part (b): y = %.4f * e^{%.4f x}\n', a_b, b_b);
fprintf('Part (c): y = %.4f * e^{%.4f x}\n', a_c, b_c);