Write it as an anonymous function, using vectorised operations:
u = @(x,t) exp (a.*x+b.*t);
then provide its parameters and variables, and see what it produces:
a = 5.0;
b = -0.2;
u = @(x,t) exp (a.*x+b.*t);
x = linspace(0,4);
t = linspace(0,2);
[X,T] = meshgrid(x,t);
U = u(X,T);
figure(1)
surf(X, T, U)
grid on
