Try this:
t = linspace(0, 50);
y1 = 100.0 - 90.0*exp(-0.0465*t);
y2 = 203.6 - 11.3*t;
y2 = y2 .* (y2 >= 0); % Set Negative ‘y2’ To Zero
y = y1 + y2;
figure
plot(t, y)
grid
xlabel('t')
ylabel('y')
That should do what you want.